{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to use backpropagation to train a feedforward NN"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This noteboo implements a simple single-layer architecture and forward propagation computations using matrix algebra and Numpy,the Python counterpart of linear algebra.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Please follow the installations [instructions](../installation.md)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports & Settings "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:10.146429Z",
     "start_time": "2019-01-14T00:43:10.144488Z"
    }
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:10.288323Z",
     "start_time": "2019-01-14T00:43:10.150442Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from copy import deepcopy\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import sklearn\n",
    "from sklearn.datasets import make_circles\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.colors import ListedColormap\n",
    "from mpl_toolkits.mplot3d import Axes3D  # 3D plots\n",
    "\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:10.293720Z",
     "start_time": "2019-01-14T00:43:10.290295Z"
    }
   },
   "outputs": [],
   "source": [
    "# plotting style\n",
    "sns.set_style('darkgrid')\n",
    "# for reproducibility\n",
    "np.random.seed(seed=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Input Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate random data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The target `y` represents two classes generated by two circular distribution that are not linearly separable because class 0 surrounds class 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will generate 50,000 random samples in the form of two concentric circles with different radius using scikit-learn's make_circles function so that the classes are not linearly separable. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:10.302487Z",
     "start_time": "2019-01-14T00:43:10.295340Z"
    }
   },
   "outputs": [],
   "source": [
    "# dataset params\n",
    "N = 50000\n",
    "factor = 0.1\n",
    "noise = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:10.310569Z",
     "start_time": "2019-01-14T00:43:10.303860Z"
    }
   },
   "outputs": [],
   "source": [
    "n_iterations = 50000\n",
    "learning_rate = 0.0001\n",
    "momentum_factor = .5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:10.328149Z",
     "start_time": "2019-01-14T00:43:10.312276Z"
    }
   },
   "outputs": [],
   "source": [
    "# generate data\n",
    "X, y = make_circles(\n",
    "    n_samples=N,\n",
    "    shuffle=True,\n",
    "    factor=factor,\n",
    "    noise=noise)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:10.331397Z",
     "start_time": "2019-01-14T00:43:10.328982Z"
    }
   },
   "outputs": [],
   "source": [
    "# define outcome matrix\n",
    "Y = np.zeros((N, 2))\n",
    "for c in [0, 1]:\n",
    "    Y[y == c, c] = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$X =\\begin{bmatrix} \n",
    "x_{11} & x_{12} \\\\\n",
    "\\vdots & \\vdots \\\\\n",
    "x_{N1} & x_{N2}\n",
    "\\end{bmatrix}\n",
    "\\quad\\quad\n",
    "Y = \\begin{bmatrix} \n",
    "y_{11} & y_{12}\\\\\n",
    "\\vdots & \\vdots \\\\\n",
    "y_{N1} & y_{N2} \n",
    "\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:10.348856Z",
     "start_time": "2019-01-14T00:43:10.332274Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Shape of: X: (50000, 2) | Y: (50000, 2) | y: (50000,)'"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f'Shape of: X: {X.shape} | Y: {Y.shape} | y: {y.shape}'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualize Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:11.123346Z",
     "start_time": "2019-01-14T00:43:10.349825Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(x=X[:, 0], \n",
    "                y=X[:, 1], \n",
    "                hue=y,\n",
    "               style=y,\n",
    "               markers=['_', '+']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neural Network Architecture"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hidden Layer Activations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The hidden layer $h$ projects the 2D input into a 3D space. To this end, the hidden layer weights are a $2\\times3$ matrix $\\mathbf{W}^h$, and the hidden layer bias vector $\\mathbf{b}^h$ is a 3-dimensional vector:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "\\underset{\\scriptscriptstyle 2 \\times 3}{\\mathbf{W}^h} =\n",
    "\\begin{bmatrix} \n",
    "w^h_{11} & w^h_{12} & w^h_{13} \\\\\n",
    "w^h_{21} & w^h_{22} & w^h_{23}\n",
    "\\end{bmatrix}\n",
    "&& \\underset{\\scriptscriptstyle 1 \\times 3}{\\mathbf{b}^h} = \n",
    "\\begin{bmatrix} \n",
    "b^h_1 & b^h_2 & b^h_3\n",
    "\\end{bmatrix}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output layer values $\\mathbf{Z}^h$ result from the dot product of the $N\\times\\ 2$ input data $\\mathbf{X}$ and the the $2\\times3$ weight matrix $\\mathbf{W}^h$ and the addition of the $1\\times3$ hidden layer bias vector $\\mathbf{b}^h$:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\underset{\\scriptscriptstyle N \\times 3}{\\mathbf{Z}^h} = \\underset{\\scriptscriptstyle N \\times 2}{\\vphantom{\\mathbf{W}^o}\\mathbf{X}}\\cdot\\underset{\\scriptscriptstyle 2 \\times 3}{\\mathbf{W}^h} + \\underset{\\scriptscriptstyle 1 \\times 3}{\\mathbf{b}^h}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The logistic sigmoid function $\\sigma$ applies a non-linear transformation to $\\mathbf{Z}^h$ to yield  the hidden layer activations as an $N\\times3$ matrix:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\underset{\\scriptscriptstyle N \\times 3}{\\mathbf{H}} = \\sigma(\\mathbf{X} \\cdot \\mathbf{W}^h + \\mathbf{b}^h) = \\frac{1}{1+e^{−(\\mathbf{X} \\cdot \\mathbf{W}^h + \\mathbf{b}^h)}} = \\begin{bmatrix} \n",
    "h_{11} & h_{12} & h_{13} \\\\\n",
    "\\vdots & \\vdots & \\vdots \\\\\n",
    "h_{N1} & h_{N2} & h_{N3}\n",
    "\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:11.126565Z",
     "start_time": "2019-01-14T00:43:11.124283Z"
    }
   },
   "outputs": [],
   "source": [
    "def logistic(z):\n",
    "    \"\"\"Logistic function.\"\"\"\n",
    "    return 1 / (1 + np.exp(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:11.155542Z",
     "start_time": "2019-01-14T00:43:11.127709Z"
    }
   },
   "outputs": [],
   "source": [
    "def hidden_layer(input_data, weights, bias):\n",
    "    \"\"\"Compute hidden activations\"\"\"\n",
    "    return logistic(input_data @ weights + bias)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Output Activations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The values $\\mathbf{Z}^o$ for the output layer $o$ are a $N\\times2$ matrix that results from the dot product of the $\\underset{\\scriptscriptstyle N \\times 3}{\\mathbf{H}}$ hidden layer activation matrix with the $3\\times2$ output weight matrix $\\mathbf{W}^o$ and the addition of the $1\\times2$ output bias vector $\\mathbf{b}^o$:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\underset{\\scriptscriptstyle N \\times 2}{\\mathbf{Z}^o} = \\underset{\\scriptscriptstyle N \\times 3}{\\vphantom{\\mathbf{W}^o}\\mathbf{H}}\\cdot\\underset{\\scriptscriptstyle 3 \\times 2}{\\mathbf{W}^o} + \\underset{\\scriptscriptstyle 1 \\times 2}{\\mathbf{b}^o}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-10T13:39:58.307221Z",
     "start_time": "2019-01-10T13:39:58.295854Z"
    }
   },
   "source": [
    "The Softmax function $\\varsigma$ squashes the unnormalized probabilities predicted for each class  to lie within $[0, 1]$ and sum to 1.  The result is a $N\\times2$ matrix with one column for each output class."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\underset{\\scriptscriptstyle N \\times 2}{\\mathbf{\\hat{Y}}} \n",
    "= \\varsigma(\\mathbf{H} \\cdot \\mathbf{W}^o + \\mathbf{b}^o)\n",
    "= \\frac{e^{Z^o}}{\\sum_{c=1}^C e^{\\mathbf{z}^o_c}}\n",
    "= \\frac{e^{H \\cdot W^o + \\mathbf{b}^o}}{\\sum_{c=1}^C e^{H \\cdot \\mathbf{w}^o_c + b^o_c}}\n",
    "= \\begin{bmatrix} \n",
    "\\hat{y}_{11} & \\hat{y}_{12}\\\\\n",
    "\\vdots & \\vdots \\\\\n",
    "\\hat{y}_{n1} & \\hat{y}_{n2} \n",
    "\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:11.163380Z",
     "start_time": "2019-01-14T00:43:11.157063Z"
    }
   },
   "outputs": [],
   "source": [
    "def softmax(z):\n",
    "    \"\"\"Softmax function\"\"\"\n",
    "    return np.exp(z) / np.sum(np.exp(z), axis=1, keepdims=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:11.170980Z",
     "start_time": "2019-01-14T00:43:11.164242Z"
    }
   },
   "outputs": [],
   "source": [
    "def output_layer(hidden_activations, weights, bias):\n",
    "    \"\"\"Compute the output y_hat\"\"\"\n",
    "    return softmax(hidden_activations @ weights + bias)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Forward Propagation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `forward_prop` function combines the previous operations to yield the output activations from the  input data as a function of weights and biases. The `predict` function produces the binary class predictions given weights, biases, and input data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:11.179000Z",
     "start_time": "2019-01-14T00:43:11.171845Z"
    }
   },
   "outputs": [],
   "source": [
    "def forward_prop(data, hidden_weights, hidden_bias, output_weights, output_bias):\n",
    "    \"\"\"Neural network as function.\"\"\"\n",
    "    hidden_activations = hidden_layer(data, hidden_weights, hidden_bias)\n",
    "    return output_layer(hidden_activations, output_weights, output_bias)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:11.190073Z",
     "start_time": "2019-01-14T00:43:11.179928Z"
    }
   },
   "outputs": [],
   "source": [
    "def predict(data, hidden_weights, hidden_bias, output_weights, output_bias):\n",
    "    \"\"\"Predicts class 0 or 1\"\"\"\n",
    "    y_pred_proba = forward_prop(data,\n",
    "                                hidden_weights,\n",
    "                                hidden_bias,\n",
    "                                output_weights,\n",
    "                                output_bias)\n",
    "    return np.around(y_pred_proba)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cross-Entropy Loss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cost function $J$ uses the cross-entropy loss $\\xi$ that sums the deviations of the predictions for each class $c$  $\\hat{y}_{ic}, i=1,...,N$ from the actual outcome."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$J(\\mathbf{Y},\\mathbf{\\hat{Y}}) = \\sum_{i=1}^n \\xi(\\mathbf{y}_i,\\mathbf{\\hat{y}}_i) = − \\sum_{i=1}^N \\sum_{i=c}^{C} y_{ic} \\cdot log(\\hat{y}_{ic})$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:11.200730Z",
     "start_time": "2019-01-14T00:43:11.191041Z"
    }
   },
   "outputs": [],
   "source": [
    "def loss(y_hat, y_true):\n",
    "    \"\"\"Cross-entropy\"\"\"\n",
    "    return - (y_true * np.log(y_hat)).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Backpropagation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Backpropagation updates parameters values based on the partial derivative of the loss with respect to that parameter, computed using the chain rule."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loss Function Gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The derivative of the loss function $J$ with respect to each output layer activation $\\varsigma(\\mathbf{Z}^o_i), i=1,...,N$, is a very simple expression:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\frac{\\partial J}{\\partial z^0_i} = \\delta^o = \\hat{y}_i-y_i$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See [here](https://math.stackexchange.com/questions/945871/derivative-of-softmax-loss-function) and [here](https://deepnotes.io/softmax-crossentropy) for details on derivation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T23:58:24.894193Z",
     "start_time": "2019-01-14T23:58:24.890066Z"
    }
   },
   "outputs": [],
   "source": [
    "def loss_gradient(y_hat, y_true):\n",
    "    \"\"\"output layer gradient\"\"\"\n",
    "    return y_hat - y_true"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Output Layer Gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Output Weight Gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To propagate the updates back to the output layer weights, we take the partial derivative of the loss function with respect to the weight matrix:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-08T04:18:37.478549Z",
     "start_time": "2019-01-08T04:18:37.476003Z"
    }
   },
   "source": [
    "$$\n",
    "\\frac{\\partial J}{\\partial \\mathbf{W}^o} = H^T \\cdot (\\mathbf{\\hat{Y}}-\\mathbf{Y}) = H^T \\cdot \\delta^{o}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:11.225315Z",
     "start_time": "2019-01-14T00:43:11.210324Z"
    }
   },
   "outputs": [],
   "source": [
    "def output_weight_gradient(H, loss_grad):\n",
    "    \"\"\"Gradients for the output layer weights\"\"\"\n",
    "    return  H.T @ loss_grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Output Bias Update"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To update the output layer bias values, we similarly apply the chain rule to obtain the partial derivative of the loss function with respect to the bias vector:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\frac{\\partial J}{\\partial \\mathbf{b}_{o}} \n",
    "= \\frac{\\partial \\xi}{\\partial \\mathbf{\\hat{Y}}} \\frac{\\partial \\mathbf{\\hat{Y}}}{\\partial \\mathbf{Z}^o}  \\frac{\\partial \\mathbf{Z}^{o}}{\\partial \\mathbf{b}^o}\n",
    "= \\sum_{i=1}^N 1 \\cdot (\\mathbf{\\hat{y}}_i - \\mathbf{y}_i) \n",
    "= \\sum_{i=1}^N \\delta_{oi}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:11.233083Z",
     "start_time": "2019-01-14T00:43:11.227863Z"
    }
   },
   "outputs": [],
   "source": [
    "def output_bias_gradient(loss_grad):\n",
    "    \"\"\"Gradients for the output layer bias\"\"\"\n",
    "    return np.sum(loss_grad, axis=0, keepdims=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hidden layer gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\delta_{h} \n",
    "= \\frac{\\partial J}{\\partial \\mathbf{Z}^h} \n",
    "= \\frac{\\partial J}{\\partial \\mathbf{H}} \\frac{\\partial \\mathbf{H}}{\\partial \\mathbf{Z}^h} \n",
    "= \\frac{\\partial J}{\\partial \\mathbf{Z}^o} \\frac{\\partial \\mathbf{Z}^o}{\\partial H} \\frac{\\partial H}{\\partial \\mathbf{Z}^h}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:11.240801Z",
     "start_time": "2019-01-14T00:43:11.234257Z"
    }
   },
   "outputs": [],
   "source": [
    "def hidden_layer_gradient(H, out_weights, loss_grad):\n",
    "    \"\"\"Error at the hidden layer.\n",
    "    H * (1-H) * (E . Wo^T)\"\"\"\n",
    "    return H * (1 - H) * (loss_grad @ out_weights.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Hidden Weight Gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\frac{\\partial J}{\\partial \\mathbf{W}^h} = \\mathbf{X}^T \\cdot \\delta^{h}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:11.251847Z",
     "start_time": "2019-01-14T00:43:11.241853Z"
    }
   },
   "outputs": [],
   "source": [
    "def hidden_weight_gradient(X, hidden_layer_grad):\n",
    "    \"\"\"Gradient for the weight parameters at the hidden layer\"\"\"\n",
    "    return X.T @ hidden_layer_grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Hidden Bias Gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-08T04:24:55.165112Z",
     "start_time": "2019-01-08T04:24:55.161087Z"
    }
   },
   "source": [
    "$$\n",
    "\\frac{\\partial \\xi}{\\partial \\mathbf{b}_{h}} \n",
    "= \\frac{\\partial \\xi}{\\partial H} \\frac{\\partial H}{\\partial Z_{h}} \\frac{\\partial Z_{h}}{\\partial \\mathbf{b}_{h}}\n",
    "= \\sum_{j=1}^N \\delta_{hj}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:11.259933Z",
     "start_time": "2019-01-14T00:43:11.253137Z"
    }
   },
   "outputs": [],
   "source": [
    "def hidden_bias_gradient(hidden_layer_grad):\n",
    "    \"\"\"Gradient for the bias parameters at the output layer\"\"\"\n",
    "    return np.sum(hidden_layer_grad, axis=0, keepdims=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialize Weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:11.270893Z",
     "start_time": "2019-01-14T00:43:11.261045Z"
    }
   },
   "outputs": [],
   "source": [
    "def initialize_weights():\n",
    "    \"\"\"Initialize hidden and output weights and biases\"\"\"\n",
    "\n",
    "    # Initialize hidden layer parameters\n",
    "    hidden_weights = np.random.randn(2, 3)\n",
    "    hidden_bias = np.random.randn(1, 3)\n",
    "\n",
    "    # Initialize output layer parameters\n",
    "    output_weights = np.random.randn(3, 2)\n",
    "    output_bias = np.random.randn(1, 2)\n",
    "    return hidden_weights, hidden_bias, output_weights, output_bias"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute Gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:11.281785Z",
     "start_time": "2019-01-14T00:43:11.272001Z"
    }
   },
   "outputs": [],
   "source": [
    "def compute_gradients(X, y_true, w_h, b_h, w_o, b_o):\n",
    "    \"\"\"Evaluate gradients for parameter updates\"\"\"\n",
    "\n",
    "    # Compute hidden and output layer activations\n",
    "    hidden_activations = hidden_layer(X, w_h, b_h)\n",
    "    y_hat = output_layer(hidden_activations, w_o, b_o)\n",
    "\n",
    "    # Compute the output layer gradients\n",
    "    loss_grad = loss_gradient(y_hat, y_true)\n",
    "    out_weight_grad = output_weight_gradient(hidden_activations, loss_grad)\n",
    "    out_bias_grad = output_bias_gradient(loss_grad)\n",
    "\n",
    "    # Compute the hidden layer gradients\n",
    "    hidden_layer_grad = hidden_layer_gradient(hidden_activations, w_o, loss_grad)\n",
    "    hidden_weight_grad = hidden_weight_gradient(X, hidden_layer_grad)\n",
    "    hidden_bias_grad = hidden_bias_gradient(hidden_layer_grad)\n",
    "\n",
    "    return [hidden_weight_grad, hidden_bias_grad, out_weight_grad, out_bias_grad]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check Gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's easy to make mistakes with the numerous inputs to the backpropagation algorithm. A simple way to test for accuracy is to compare the change in the output for slightly perturbed parameter values with the change implied by the computed gradient (see [here](http://ufldl.stanford.edu/wiki/index.php/Gradient_checking_and_advanced_optimization) for more detail)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:11.523510Z",
     "start_time": "2019-01-14T00:43:11.282843Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No gradient errors found\n"
     ]
    }
   ],
   "source": [
    "# change individual parameters by +/- eps\n",
    "eps = 1e-4\n",
    "\n",
    "# initialize weights and biases\n",
    "params = initialize_weights()\n",
    "\n",
    "# Get all parameter gradients\n",
    "grad_params = compute_gradients(X, Y, *params)\n",
    "\n",
    "# Check each parameter matrix\n",
    "for i, param in enumerate(params):\n",
    "    # Check each matrix entry\n",
    "    rows, cols = param.shape\n",
    "    for row in range(rows):\n",
    "        for col in range(cols):\n",
    "            # change current entry by +/- eps\n",
    "            params_low = deepcopy(params)\n",
    "            params_low[i][row, col] -= eps\n",
    "\n",
    "            params_high = deepcopy(params)\n",
    "            params_high[i][row, col] += eps\n",
    "\n",
    "            # Compute the numerical gradient\n",
    "            loss_high = loss(forward_prop(X, *params_high), Y)\n",
    "            loss_low = loss(forward_prop(X, *params_low), Y)\n",
    "            numerical_gradient = (loss_high - loss_low) / (2 * eps)\n",
    "\n",
    "            backprop_gradient = grad_params[i][row, col]\n",
    "            \n",
    "            # Raise error if numerical and backprop gradient differ\n",
    "            assert np.allclose(numerical_gradient, backprop_gradient), ValueError(\n",
    "                    f'Numerical gradient of {numerical_gradient:.6f} not close to '\n",
    "                    f'backprop gradient of {backprop_gradient:.6f}!')\n",
    "\n",
    "print('No gradient errors found')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:11.526941Z",
     "start_time": "2019-01-14T00:43:11.524522Z"
    }
   },
   "outputs": [],
   "source": [
    "def update_momentum(X, y_true, param_list,\n",
    "                    Ms, momentum_term,\n",
    "                    learning_rate):\n",
    "    \"\"\"Update the momentum matrices.\"\"\"\n",
    "    # param_list = [hidden_weight, hidden_bias, out_weight, out_bias]\n",
    "    # gradients = [hidden_weight_grad, hidden_bias_grad,\n",
    "    #               out_weight_grad, out_bias_grad]\n",
    "    gradients = compute_gradients(X, y_true, *param_list)\n",
    "    return [momentum_term * momentum - learning_rate * grads\n",
    "            for momentum, grads in zip(Ms, gradients)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:11.540161Z",
     "start_time": "2019-01-14T00:43:11.528431Z"
    }
   },
   "outputs": [],
   "source": [
    "def update_params(param_list, Ms):\n",
    "    \"\"\"Update the parameters.\"\"\"\n",
    "    # param_list = [Wh, bh, Wo, bo]\n",
    "    # Ms = [MWh, Mbh, MWo, Mbo]\n",
    "    return [P + M for P, M in zip(param_list, Ms)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:11.548546Z",
     "start_time": "2019-01-14T00:43:11.541509Z"
    }
   },
   "outputs": [],
   "source": [
    "def train_network(iterations=1000, lr=.01, mf=.1):\n",
    "    # Initialize weights and biases\n",
    "    param_list = list(initialize_weights())\n",
    "\n",
    "    # Momentum Matrices = [MWh, Mbh, MWo, Mbo]\n",
    "    Ms = [np.zeros_like(M) for M in param_list]\n",
    "\n",
    "    train_loss = [loss(forward_prop(X, *param_list), Y)]\n",
    "    for i in range(iterations):\n",
    "        if i % 1000 == 0: print(f'{i:,d}', end=' ', flush=True)\n",
    "        # Update the moments and the parameters\n",
    "        Ms = update_momentum(X, Y, param_list, Ms, mf, lr)\n",
    "\n",
    "        param_list = update_params(param_list, Ms)\n",
    "        train_loss.append(loss(forward_prop(X, *param_list), Y))\n",
    "\n",
    "    return param_list, train_loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:43:11.559368Z",
     "start_time": "2019-01-14T00:43:11.549787Z"
    }
   },
   "outputs": [],
   "source": [
    "# n_iterations = 20000\n",
    "# results = {}\n",
    "# for learning_rate in [.01, .02, .05, .1, .25]:\n",
    "#     for momentum_factor in [0, .01, .05, .1, .5]:\n",
    "#         print(learning_rate, momentum_factor)\n",
    "#         trained_params, train_loss = train_network(iterations=n_iterations, lr=learning_rate, mf=momentum_factor)\n",
    "#         results[(learning_rate, momentum_factor)] = train_loss[::1000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:54:41.868647Z",
     "start_time": "2019-01-14T00:43:11.560532Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000 12,000 13,000 14,000 15,000 16,000 17,000 18,000 19,000 20,000 21,000 22,000 23,000 24,000 25,000 26,000 27,000 28,000 29,000 30,000 31,000 32,000 33,000 34,000 35,000 36,000 37,000 38,000 39,000 40,000 41,000 42,000 43,000 44,000 45,000 46,000 47,000 48,000 49,000 "
     ]
    }
   ],
   "source": [
    "trained_params, train_loss = train_network(iterations=n_iterations, lr=learning_rate, mf=momentum_factor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:54:41.871301Z",
     "start_time": "2019-01-14T00:54:41.869676Z"
    }
   },
   "outputs": [],
   "source": [
    "hidden_weights, hidden_bias, output_weights, output_bias = trained_params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot Training Loss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot displays the training loss over 50K iterations for 50K training samples with a momentum term of 0.5 and a learning rate of 1e-4. \n",
    "\n",
    "It shows that it takes over 5K iterations for the loss to start to decline but then does so very fast. We have not uses stochastic gradient descent, which would have likely significantly accelerated convergence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T03:37:41.373984Z",
     "start_time": "2019-01-15T03:37:41.093344Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = pd.Series(train_loss).plot(figsize=(8, 4), title='Loss per Iteration', xlim=(0, n_iterations), logy=True)\n",
    "ax.set_xlabel('Iteration')\n",
    "ax.set_ylabel('$\\\\log \\\\xi$', fontsize=12, rotation=0)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Decision Boundary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following plots show the function learned by the neural network with a three-dimensional hidden layer form two-dimensional data with two classes that are not linearly separable as shown on the left. The decision boundary misclassifies very few data points and would further improve with continued training. \n",
    "\n",
    "The second plot shows the representation of the input data learned by the hidden layer. The network learns hidden layer weights so that the projection of the input from two to three dimensions enables the linear separation of the two classes. \n",
    "\n",
    "The last plot shows how the output layer implements the linear separation in the form of a cutoff value of 0.5 in the output dimension."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:54:42.993024Z",
     "start_time": "2019-01-14T00:54:42.368483Z"
    }
   },
   "outputs": [],
   "source": [
    "n_vals = 200\n",
    "x1 = np.linspace(-1.5, 1.5, num=n_vals)\n",
    "x2 = np.linspace(-1.5, 1.5, num=n_vals)\n",
    "xx, yy = np.meshgrid(x1, x2)  # create the grid\n",
    "\n",
    "# Initialize and fill the feature space\n",
    "feature_space = np.zeros((n_vals, n_vals))\n",
    "for i in range(n_vals):\n",
    "    for j in range(n_vals):\n",
    "        X_ = np.asarray([xx[i, j], yy[i, j]])\n",
    "        feature_space[i, j] = np.argmax(predict(X_, *trained_params))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:54:43.989441Z",
     "start_time": "2019-01-14T00:54:42.994091Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a color map to show the classification colors of each grid point\n",
    "cmap = ListedColormap([sns.xkcd_rgb[\"pale red\"],\n",
    "                       sns.xkcd_rgb[\"denim blue\"]])\n",
    "\n",
    "# Plot the classification plane with decision boundary and input samples\n",
    "plt.contourf(xx, yy, feature_space, cmap=cmap, alpha=.25)\n",
    "\n",
    "# Plot both classes on the x1, x2 plane\n",
    "data = pd.DataFrame(X, columns=['$x_1$', '$x_2$']).assign(Class=pd.Series(y).map({0:'negative', 1:'positive'}))\n",
    "sns.scatterplot(x='$x_1$', y='$x_2$', hue='Class', data=data, style=y, markers=['_', '+'], legend=False)\n",
    "plt.title('Decision Boundary')\n",
    "plt.savefig('boundary', dpi=300);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Projection on Hidden Layer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:54:43.994077Z",
     "start_time": "2019-01-14T00:54:43.990630Z"
    }
   },
   "outputs": [],
   "source": [
    "n_vals = 25\n",
    "x1 = np.linspace(-1.5, 1.5, num=n_vals)\n",
    "x2 = np.linspace(-1.5, 1.5, num=n_vals)\n",
    "xx, yy = np.meshgrid(x1, x2)  # create the grid\n",
    "X_ = np.array([xx.ravel(), yy.ravel()]).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T00:54:44.635654Z",
     "start_time": "2019-01-14T00:54:43.995119Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6, 4))\n",
    "with sns.axes_style(\"whitegrid\"):\n",
    "    ax = Axes3D(fig)\n",
    "\n",
    "ax.plot(*hidden_layer(X[y == 0], hidden_weights, hidden_bias).T,\n",
    "        '_', label='negative class', alpha=0.75)\n",
    "ax.plot(*hidden_layer(X[y == 1], hidden_weights, hidden_bias).T,\n",
    "        '+', label='positive class', alpha=0.75)\n",
    "\n",
    "ax.set_xlabel('$h_1$', fontsize=12)\n",
    "ax.set_ylabel('$h_2$', fontsize=12)\n",
    "ax.set_zlabel('$h_3$', fontsize=12)\n",
    "ax.view_init(elev=30, azim=-20)\n",
    "# plt.legend(loc='best')\n",
    "plt.title('Projection of X onto the hidden layer H')\n",
    "plt.tight_layout()\n",
    "plt.savefig('projection3d', dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Network Output Surface Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T01:41:34.001050Z",
     "start_time": "2019-01-14T01:41:33.995221Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(25, 25)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zz = forward_prop(X_, hidden_weights, hidden_bias, output_weights, output_bias)[:, 1].reshape(25, -1)\n",
    "zz.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-14T02:05:28.390936Z",
     "start_time": "2019-01-14T02:05:27.778469Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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q7ofNUeO+dvt+4vE4pmn6bhN7GRHfisC37/AiIKh9gieUOKoEdRApvkZLn8Y/rZY+3kwhRVF2bfA8CAx6YOEgjt+vzVGnFF83jcapVIrV1VWy2WzfKr5O/U+Bb9/hREBQLdirkm9QDYCDJqi9RFDdWPpomkY8HieTybS19Bm0SGVQGCRB7XXAYD/78twmvNphL9jpOIFv3+FEQFAt2AtB3WgRTC/oRiiyF0uf3TBoL76jhn5TfO0ItZdozHObuHTpEpubmzu6TbRitxR84Nt3+BAQ1D5h0L1Qh8WL7qAsfXbDYbn+a43DnuJrvR8syyKZTG7bV6+2RbIsk8/nd3SbaEU3acHAt+9wISCoFuwlghqkiu5ao5Olz6VLlw7M0mcnDDqCGuTI90Edt3Gx3ylN690PqqpSLpdxHIdUKuVv2ytBeaS8m9tEK7oVMXmRVKVS8WudAQaDgKBacD27SRzEVNl2IoXG3qFGS59KpcKZM2f27di94LCbxd4ox/eamjc3N6lUKszMzHRM07ZaPDmOQzQaZWFhAVmWicfj/s/7Iajd3CY6bdcNvP0Hvn2DRUBQ+4TDQFCeEqlX65ZuLX2i0eiOvUNeHWpQY9eDFN/+YacXEy+iUBSFsbGxntO0jWawkUik5wiq8fd3cpvYKwRBwDAMZmZmuOmmmwJLpAEg+MRbcD1HUJ6Sr9ODtFdLn90wyF6wQRPU9Zji261eGAqF/GgonU43qSfz+Ty1Wq3n9JdX45mcnGR+fp7x8fGeSbb1HuvkNtF6rf3A+ywC377BIPi026CfxW7QTgqwpeQblKXPIAnqMNhNDQq7Le7djgDp5cVkr8MKZVlmfHycpaWlnr+3dhFXo9tEO9PeflWHXg1NEITAt28ACAiqDQb9Nt4N2ln6bG5uUiwWt9UCrpWlzyBJ+qjWoBqjD89doxsZ/15HgPTTqNt6vl7kMz8/39OwzU4pQc9tYmlpifHx8abz66ex19tOkqTAt29ACAhqH+Epyfbz5m219PHehIFtlj6yLBMKhRgaGtq34/eCo0pQ1xqNablSqUSlUvEX/kZ3jf2U8bdiv6yOIpEIkiR1jHzaYadnrNFtYmRkpIm8+4l8LMvyXS4C375rj4Cg2mCvdaheFT+9WPokk0kURWn7cFSr1YGP3BjU8W80gurW9FZRFNLp9DX3kOtnHlOnYYVeL1O7yKfTsXciB89tIpfL+dZXe42gPAS+fdcWAUG1wUER1H5Y+uwESZL86GoQOMoR1F4c8Nul5RqFKzuZ3lYqlYE4sveb4mu3H1EUSaVSZLNZ1tbWyGQyO26zG9l4bhMLCwsUCgUSiUTfmY12qcfAt+/aISCofYRHUAdp6bMTrge7o4PCoBt1d4N3T1SrVf9+0HV9z8KVw9Ko2y8aiSOTybC0tMTGxsY2t4nWbXaL3gRBaJKz7yXF17pd4Nt37RAQVBv0Y+FSq9UoFovkcrmmBtaDrgU0YtCGsUc1xed9rzulanvpJ+v3+NcS/bqZt/uZR1Be5DM/P48sy8RisY7H7oYcPTn73Nwc4XC4L0eITscKfPuuDQKC2gXdSnSHhoYIhUIYhsHY2NhAzjUgqL0RVONCCbS9Fs+yybKd+n+LSLLCzafj4ICDQ6g+/sP9bxeWeTDTjgc5sHC/IyhoJhVJkvxRKjttsxM8t4mZmZm+3SA6fb6tvn2apgUktc8ICKoNHMdhenq6o6XPThLdQdaADgNBDWrsfC/pRVmWcRAQBBAFAccBy7YxLBvTtlFlCU2WkCQJs542lEQR07IpVHRym2VWC2VWN0uENY37zkxSrun80zevIokCAgKiCJIgMhTTuO1YmmPpOI5tN30/oijWzxts3HMRANtxEAWXIHe7pkFFjf3WoNo5mbc+S7tZGPWarlMUhUgkQi6X2/dm28C372AREFQbSJLExMREzymYQbtJDDKC8Y5/PRi22g7UTJOIqrBR0tEtk4gqE1JkQqpMzbDIlaosrW9SrNS458wUT3/nMi9Or7rCFbbuiZvHNb768ixvvfMmHrxlkqdfmvX/LaTK3BTRUCSRctUgrCmIsoAkiliWTblmkC+XyRWrrBer6IbF7SdHGEtGWc6XySTCyKKAbTsIONi23fYar5cIqtOwwnbnv5OFUT+CB0EQGB4eZmFhgWPHjnW1fbckHPj2HRwCguoATdN6fjsdNEENOr0wSJFGN24KXs0wmUrxtVcXedPpURIRDVB4+jtXWMoVWS9WmcykGEuGyRVrzK0WKBk23/2GU6wXdbL5StN+VUVCNw1evLrEvWenmEzHkAQBTZERRYGablLWTVYKZZZyRe46Nc7qZpEvvnBx2zmOJmO8MreGLIlENZlPfvk7pGIap0aGODk6xFgy6l+Ll2I8dfNpBMGNBoV6VOjUf0dAwLatA3lp2W8VXzs0Whg1kko/BGVZFpFIBFEUfUuk3c6/l+bhRpISRTGwRNonBJ9iB/RrdzTICGbQOAxKut3GPsRiMSRR5LE7jrOSL/P5r77Cex84y5nJDBeWN1FUDVEE3bBIxTTm1+DV2TVG4mF+8LvO8u2rWTKJMEMRlbCmoskiDlCq6ixvlBgZivDSzCqvza+zXqySSUTIJEI4Drwym2Umm+e/PHQr33VmgucvLjaduyqLyJLIxcUcD5yb5KcfewOG5dTTjSJV3aRqmKxvVsiXdcaSEYZjIT7/9dfRTRvdstBNG8cBWRS46/Q4d54cPZDU70HVoFoRiURIJpMsLi4yOTnp32P9TNOVJGlHt4lO23QL90VBCHz79hHBJ7iPGHQE453DoArn1zLF12h860m3vXlUO9n6yLKCZdt8Z3qV5y4uAfAPX7/Ijz58jvtOj/PNK0uMDUUZT0ZIRkPcedMomiyhyBKO43D3zWPMrBa4spJnfbPKUETjuYuLFAoFhlMp3nRmgttPZvjPKyuuQEIAw7QJqRKKLLJRqvHP/3mFt99zM1FNQVUkhqIhIpqCpkgICJR1g+UNN8VXqlX50jevsL5ZIaQq3DyW4JXZNUzLRhLgvQ+d53vuvIm/f+a1ps9HkkQqNZNnX53h4dtO7Ht0v58qvt1IIJFIYJomKysrjI6OAr0/a43n6/Vcra6uMjIy0nGbfpp7RVFE13Xm5uY4fvx44Nu3RwQE1QH9LvCDJAjY3dH8oI+93wS129iHRil/rVbbcR6VJCtUDYuX59e5slLwfx4LKWyUa9x1apR7T4+hmxblmkm+XKOqm1xaWmclX8K0HP73R9+AJAg89/oiEU1GU5o/5+cuLpJOhHjPg7fwqX9/mfFEhPFUlKGoxp0nR1FlCVWWsB2HW46lWc2XmV0tsLZZIaIqzKxtslFyhTZjyQg/eN8Z0vEwq4UKkihgO6ApEqZlYznw1//zOf6vH3qE9z54C2ubVZKxEFFNIaTIyLKIbTuUqjohVUZRlH0TsezXPW7btm8ltBNSqRQrKyusr6/3fazG881kMiwvL7O+vu67TbSilxRf63amaQa+ffuAgKD2GZIkYZpmVw/dQR1/UATVbwS1l7EPjei0YEqShCCKXFjcYDq7STSkEFFl7rr9OMczcRRJZGG9yPzaKrefyPD1C4uUazpXl/PcfnKElXyZqu5e1+efu8D/9vB57jszzsWlDSzHRpVFzh3LcPb4GOlYmHhYJaTI/PTb7sSyHco1g0KlxmqhwpWVHCv5EuWqyVvfeIrjmTiff+4Cpm1z+8lRKrWtKGd5o8xXX5nj0VuPkStWiWoKx4fjnBodIqIphFUZTZZAgHQiSjSkMr2S5/JSjkrNJBpSyOaLzC3nOHssw2N3nd7XfrFeCKrTMXsRIoyOjrKwsLAv6cp2bhOt2AtBybKM4ziBb98eERBUB+zV7mjQBDUI7FaDOoixD7tBkmRkWeKFyyu8OLPGW+84TiYeQpMlVgplnnt9kdcWc9h10YEoCjx4yyRfeXEGByhXTTKJKHOrBSKazHgqymqhzL2nx7n95AiKJPHmN5ygpptsVnVyxSoz2QL5So3vuf0EC+tFXplbYzFX5PxUmumVPN5a/eVvXeG9D93Kex86z3//2iuIooBhWxxLx5lMRckkIsTDKg4OP/RdbmRY0d3Ibnolz9pmhQvT86CGOTWW5PveeIorK3lmsnmGY2E0RSKkuvfhhblVbjs5zngqijmAVgBvBEw7yXi3i7dHKlevXvVthrpBJ3L03Ca8nqvW/XUb3bXCI7bAt2/vCAiqA67XwYWDJii4tmMfujgpFnIlzo4nueemEWqmxXS2wEuzq9sUeQDPvLrA2FCER287xqnRIYZjIWJhFUkUEQWBim6QL9eYXy8yORzjPy4t8cLFJXL5PMOpVNO+/uk/LvOD33WGfMklFMt2iIU0Nis1VFnkWDrBar7E+eMZfvqxOxBFkQfPTWGYNsWqzkapysXFdVY3K9x+YoR0PMy3ry6zUdKZyeYBWCuUyGQiXF3O8/zFRb7v7lP89//vZSTJ7dvSGkj+n194jR97690Hdo/uFAl7mYVMJtNEBP2ILUKhEKurq0iSRCgU2vX3dxI7NA5PbN2fZVld7b8V7RzQA9++/hAQ1D7jKBFUu8WoVqtx5cqVazb2oRHt6n+CAF99bYl8Wedttx/jRDpKoVxDt5ojvVhI5s6bRjmRSZCoRy0nRhK8MreGJIrMrOaZaahbAfzQm85y+8lRXriw1PZ8ljbKvDq3zh03jRAPqwzHw9x3ZhxFEpEkkZphsVmucXExx81jSVYLZb7wjcsY1vYodHa1yI8+cp7bT4zw/MXtxxsbiiIApuXwww/fxvJGCVEQEEWBkyMJ39GiUjOIhffWp+M4bk/W5uamL1JpVEo2RsKewa3jOJTLZRYWFvzfgd4l4x7ZjI6O+sq+3aKc3cQOsiy3bQzu1wHdNE2f2ALfvr0hIKgOCCIoF92OffAc2K9evcrp06f37fi9oD1BCVRrJqokYdk2Fd3krlOjLOfLRBSZO05kGE9FCSky68UqFxdzFCo6ODaP3nYc3bBYyOWJt1nULy7leGNI4YmHzvHUM9/hthMjjCXDW6o8WUIUBHTL4qaxIa4sb1AzbF6dW2WtUMJqyDwtnRjh4VuPMZ6KMru6ue1YtuPwv15f4LE7TnL/LROcmxqu17okVEXGsmxX6p4rMpmOEw/JlCo1RFHCsgycegozu64Tnxrp6j71UrKNKknPad00TcrlMpqmkU6nu4qEZVlmYmKiiVj6IShRFFFV1a8hHTt2bMdaUTdycUVRGBsba2oM3ksNqnG7wLevfwQE1QF7IahqtbrPZ9M9vAehV+x17IOHQaoY2wkABKBq2sRCCrGQwpXVTaaGIrzz7lM4wGKuxPMXl7i4tIFhupHLiZEElm3zz9+e5u133cTKNy6hKRKaKpEMh5jKxBkdijA6FEESReJhlZ95x5soVt3038JakbVihWyhTCoaplSt8cC5KUYSEb4zk2WjVG0iJ4D1YpXX59f5vjfexFPPX2QoqjGejDEcDxELqWiKhCKJ6KZFRFPQDZNXZ7NcmV+haotU9C2yecsdJ5kajvO/XrpMKhZmenmNYnnLguu/PvEWlAaC6pSS7eS0DnDlypW+PCdVVfWjn6mpqZ7l6o2EFgqFSKfTfuNtJ6LrNhIKhUJNjcH7RVAQ+Pb1i4CgdkA/iqfDHkE1jn3wBAv7MfbBg+eJd1gIqh44IEsCsZDCS3M5LMshGdNY36zyhW9cbrMfl7DXChVyxSrvuOc0tuPw0PljWJbtElGpylKuyKXlPKZp8X1338w3Li/z2nyzDDodD2PbDl94/gI/+ugbOD+VZmG9yFqhTCKicjyTYGwoxlgqiqZIiKLA4286i25a5Ms11otVLi1ukN0sE1IkbMvh1NgQt9QFFxfmVrbNT/rO1RXOHctgOQ6mbaMpCkVq2LaFaVmYlo0o2li2zZXLl3uexNtv6stDOBwmlUqxuLjYM0G1HjsWi2FZFktLS0xMTLTdVy8Nt5FIhFQqxcLCwr7OkILAt68fBAS1zzgMBGWaZtv6UOvYB+9h3M+Bd57UfBCy2lYVoes67v63IklEVImlfJnJVATdtEmEVb77tin+/eV5f5vxoQh3nxplKKKhyRLrxQq5UpVEWOXrr8/zrSsrOA5EQgoTy6sbAAAgAElEQVSnRpNcXs670dZ/XOB77znLaqHM2uZWBC0iEI+oTAzHyJerjCdjPHH/LYii+3m7/VZV1jYrrG1WmM4W+J7bTwDwueea7ZBOjiSwbItsoYIk5nj8gfP8t9mFbZ9DNl+iUjM5PZlhfnkNSYTV1SwIArIsYzsOr08vcfbEGGfPnu35JWw/bI7i8TiGYfTc19Tu3hoaGsIwjG1j3j30Sqie28Ta2lrfL1s7OaAHvn3dIyCoHdBPBOURxLVAu/qQVy/wCrWqqhKPxxkZGfFHRRwkDtNUXVEU0eshVCwk4zhQrJqosohh2fy/35rmie86jeNAKhYiEw8jigJrmxVensnyzatZDNNCEgV+5JFb6zLxTXLFCpos++QH8J+X5nnDTRO8+01nWcwViYc1wqrsN+WWqoarylvKcWYixTOvzPHiTNbf/rYTo8yuFihWDZ564RI/+vB5HrvjBP/6nRn/dyRRpGo7KJLA6maFk2ND/J+PP8pn/v1brG4UsUwD23Gl8ku5TU5PjXF5foVYJEQms+WYYNsOiiLzH69Oc8+5k1hWb/frfhnFplIp1tfXWV9fJ51Od7WfTi8/7ca8N27Tq1w8mUyyvr6+q9tEK7pZLwLfvu4RfDI7YD/fnPaCRluf3epDiqIwOzvLqVOn9v08usFhIihBEDDrirjhqIZerzGpkohu2qwVa7w4s8Ybb8owv17ky9+ZZia7yamxIUo1HcN0U6WW7fDU8xf54YfP8+D5SV6ayXJmIkU6Fuaem8dclwa57u5gO0ykYnzr6gqrmxViYZXp5Q0KZd0/LweHB88fY2Y17/9clgS/SbdmWHzlxRnecffNqIpETTdJRkMMRTRURcKxHXTLolypEY+E+D++9z6y+TIvTa9wZXkD23FY3Sxz8/gwgiBtc7uwbZtoWOVLz17mtlOThFS5J2HNfhnFCvWIrlqtdmyWbXfsdgv6To23lmX1nE7zSM2yrB3dJtpt1w15B7593SH4VA4I/aQGdrL16bY+5EmAB4VBElS7mVCeZDsZVTHqi7AiSz75bNYMbMdhKKIxu1rEoV6DariEkCpz58kRLMuuN9HG2KzobFZ0FnNFVgoVLkwvEI0nUGSJH334HOlEmBcuLXPbsTRWyzlNrxQIqwrveeA8X/jGBY6lE5yeGOaWiVTdn09GEKCiGxxPx5lfXmd6MUtIkXl9dglFlpEkicX1Td73/ffzl//0HLffPMm9Zyd58x038fr8KqZlsVoo8YabJ1lZ32g6vmU7ROoL9r++8DI/8PBdQPcE1a9RbOsz4f231ywryzKRSGTHfexUT+q0r37dz2VZ3tVtot123da7vGfFa+QNfPu2IyCoHdDvW+JOdkO72frsdSz4oJVBhy2C0utElIxolGt1gpJEilU3comoMhslHU0ReeudJ/jnb03XUzAiD94yyc3jSWIhlVypyrdnsgyFNc5MpHhlbo2ljRLZQgXLtqnqJlHAMC2eev4S733oHHefGkU3LWzLZjwVZSrtqv+SdRm6LIo8cf95ilWdim4ys5Ijmy+zUihTrBrIkswTD9yCKMu8cGGe88eGqegmlg3DCRXdtJBFEdu2+M8Ls/znhVlGhmLce+4EN42PYtsOibDGyvoGcr1xF8CybGJhl6BmlteZz+aYzAx1HUXtV43R209js+z4+PiO0c5ux263r15dyb3jeCnxndwmWtGr8s97XgLfvvYICGoH7EVqbhjGtoioXTPj0NAQmqbdMCH+YSOomuEuuvGQwtWs218kiwK1OnGFVZmaafGlb03zIw+e5fvuOsnYUISQqlAo13htYZ2X59Yo11zpflRTSEQ07jszwf945lX/WA4OkgiTw26EVazUuPf0OLbj8PCtxzAtm81yjbVCmZezy8SiIV6ZWeGHHjhPtuAaxr46n/P3J8tuzeTfXprhvzx0nrFUDBEBy3IoWwZjkruQ6aZFJKRSrLiEm80XeeG1GTKJCFcXV7jj9HEs20FVZEzL/R3Ltt1R9aKIZdt8++IME5k7u/6c98vJvJFsZFlmfHycpaWlbQMKO23TCa39Vv2oDhuJZie3iZ226xae20QulyOZTAaRVANujFVxgGg39qFUKlGpVHyT02tm61OHp2YbxNvYIGditRO11AwbRRLdURf1eo8kCn49KqRIrqND1eDScp5bJpJczRZ4aWaG2bXtDbOlmsHriznuDik8fv8tbJSqxEKKX4fSTYtCqcbi+iZrSoWbRpP8309/m1xJRxQlvHX9lqlhREnmCy9c5N33n6NmWk0E5WG9WOP1hRxvu+cc37owjWnZ1EwLSRIRBHduVVjdIihwU5KGafLcy1e44/RxRFFAU2XK9ajRdhx00yQW1siXXMlzL3SzX7OgWvfTaUBhI7q9rxv7rboZ6dGKVlLr5DbRbrt+XjYlSWJ2dhZFUYjH4wPPhBwWBAS1Axpvkl7GPuTzeVRVJZlMDuS8vRTjoAhqkBFU47Ftx6FmWgzHNHdhr0dToihQM+oEpcq+UKFUM1wJuSpTqm01OzuOg23ZGKZJWBY5N5kkFnIjnLAh8c1Li8ysrLOpOyC4kYmHd79J5fEHb+VvvvJi07lulnWS0RAXF9d5cWaFO06OslaoUKrXxCzLwXHAcmxen1/n7ESKyUySl6+uuNdmOyiyRM0wCGvNi6WmyNQME9t2sB0HWZIJNajYbNvGNG1i0RD5kjvGoxeGOshpuu0GFDail/va67daWlrquSbcLhJq5zbRbrt+jaK9+zfw7dtCQFA7wHEcrly50vPYB0VRBt4LtZcHZS/wfMcGgdYIynGgalpk4m5KplpP64mCQNVwvx9Fak73ZQvuoMCRuMbluSVMwwIcJjNDPPHAbYynYixvlPjW1Swr+TLf+8aTFKomMysbZFql0gJcXt7gtuMZHr//LE9/Z4aRoQjpeJjhWIjheJg3334CWXLnNj14bgrT2lr8BYGm6GYyk/IFF7Zjo8kSVcMkpDV/zyFVQdddonMcVxSiqQ0E5TgYpkUs7H4ukthb+8F+ycw7EV0ikcAwDH9AYTthRbeIx+Nks1mWl5d3naDbiE7PT6vbROvn0OjD1wu8zyLw7WtGQFA7QBRFTp482fPDKMsytVpt9188IAzS0XzQEVQzQTnohktQLik1EJRuUqlWkQSBfKnM6uoqojNOoVyjato8dP4Er82vczwzxEO3HmMoojGdLfCZZ16lptucmUgxu7rJi9NZ3nH3zVxdWPGPOzIU4Xg6xuhQlJFEBFkSSIQ1fuSRW6mZpjsfqlhhdaPAhbkskigwPjzE+HCCTz/9H22v7fyJMd5y11kEwAEsy3El6DWDkNr8GIc1N4JybAdBcAmq8Xds28Gw7C2CknpL8R1kBOVheHi4Y19Tr2QqSRKyLPfU07STsKLRbWJqampbpmUvM6QC375mBAS1Czwn5l5wGNwkjiJBbZeZC1R0k3TMVYVlV3Os5jYRxXMUimUs00SRJWxHJJPOEI+E2ajUWMhukomFeP/b7kISRV5fWOepFy5SrrrfaTSkYDkuQTz7+iJjqRj/9Qfux3FAlSUsx6ZYMdgoVVhYL3BhcZ2p4Tinx1P81f983j+7U2NDGKZNMhqiUKlxUu38OOr1lN3UyBBz2TyGZaHKMhXd8Gc+edBUhWo9gpJEEU1x62MebNtNV8aj7uciiWJfi36vaD3GTpGY19c0Pz/v12X6gXeMTCbD0tISuVyOVMtYlHbYjWg8t4mlpaWmyKxfgjJN098u8O3bQkBQu6BfP75BEQQcPYLyZPvlchnTNMnn85imybnzt1Kq1EhFNURBQFA1MhnN7XOSJLdBUhLd0RsCqLJITbcQEFjMFbl5LMlf/Ot3fKm6f431xUKVJWq6gSq7daeXZ1b55pUlynXjVlUSuWVymKvLeRZWN3nDiVGOjyaZXXH7ktY3KxzLDCGJArliBXmnha1+D54YTTGXzVPTTTRFplozCLXIssOqQq4+60oQBMIhDUEUEAXXm9B2HHTDJB5xIyiPJLr97g5CxdcOnsR7fn4eWZb7ns0k1gl4fHzc39duhNdNrSuVSpHNZpsis71GUB4C3z4Xgeh+F/Tz5hJEUPtPUJ6tU7FYZG1tjYWFBa5cucLFixeZnZ0ln3cH+GmaxtTUFKdPn0YQIBrWqJk2ggD1DB+iIPg9UZIo+E7giiy69aj6V247DlPp2LZz8epCqizxzntOo8oSr0wvMZmO+eTkfRbesqxbNhcW1nn4DVsOH/myjojbOFso11Dkzo+jg+s8MDniCm+quokmy1RqOqrSvCCGVPfn3ucWC6nYluPXoSzbQddNYuEQiuRGnb28g+2Xiq8bRZ4kSUxMTLCysuJHFP0ewyO8XC5HpbJ9WGUjuiWaTCbjS8Q99LNmNEZQjfvxLJG8gZ9HDUEEdQDoJ+raT0iSNLAbeq8EtdP8qd36xzY2NjBN0y9uC4JAWJMpVnVCShgHkESXf7zRGm49yiMrkaphIYnujCUBuGVymCvL+eZrFAQEAe4+NcLIUJi//beXyGbX+KUffgujiQgrhbJ//Mb74PkL8/z4W+4gFQuTK7oLpGHZiKLAZrnapP7b/rnYOLZNOuE2ipZrBoosUtUN1BY1WUhVfIICCGsqlm2jqTKVmoFtuzLzaEhDUWRs2+5JfLCfNahuJNmKojA+Ps7i4mLPEu5WovEIbze5OHRHNI2pyL2Qdic7pqPu23e0rrYP7OVBHNTYiUFGUJIkdUVQ3jC8xv6xdv6Cw8PDqKra1dvsNjdzIK4plHXTN3aNaYqrbqvHNqIo+FGPLLriiVhYQpVFVjYrHEtvTwUJAowORTiRSfA/nnmFqm6imwaLuSJvOjvBP37jkrtvgabIpFg1mFvd5LvfeJr/52uu7Lyqm4RUGdNysG2HZCzMRnH7272A4J6xA2OpGMu5oiuX142m+hJASJEpVb0ICjRVxrQsVEUBKtiOjWGYqIpESFWw6nL0bu/UbiOoRteUarVKLBZreh566dXzvCZXV1d72q7d7zYS3k5Nwd1CEAQmJyeZm5vr+8XUNM2ONk9H2bfv6Fxpn9iL3VE/Fiv7gUES1LZepB6H4e3lLbQ1YrEdh3TcFSCYdVfzaMhdkB0HZFFEAF9m7pFVPKKhSCLTq0XSsRAnRuLMZLeado9n4pweT/LyTJb14tZojX9/eYYfeeQ24iGVzapev3eaF6wLC2t8z503EVZkKoZJzbQI12XiNcMknYi2JShwFXnFcpWTY8Ms54pYto3tuLWzRmiqO03X206W3AZiT8ln2w6CKFLVTYaiYSzLxnZs5D4X/W6iXsMwqFarjI6OdtzPblBVFVVVd5z91O5c2z2DOzUF9/NiKYoiIyMjzM/PU61We66X7dbge1R9+wKCOiB4YzeOCkE1NjLrus709HTHRuadhuHtBY0E5c6CchiOaazky74PXVSTXYIC4iH37x626lECsiRSM0xWNyucm0z7BDWRinL/2Ukuzq9RKFfdqKN+KflSjY1SjfvOjPPNy8ucGEkwkYxxZmLY999ze5Mc7j47xTMvT2M77nEBqrpBKhZue222a2PL0lqeqZEkvDqDbbv7ao2gVFmmXHeWcNgSKHg1KNt23Gut6SRiYQqlCrbt7FqRbiQiL51aq9V2nbrsRcutKrpea1m2bRMKhRAEgWw220R2nbCT2MFrCm6Vi++lyT0ajbK0tMTk5GRPs566WSuOom9fQFC7YC9+fKZpDkR9c5AE1c0gRFEUmZiY2NdBiN2gkaBEUcQGlLpQwXM1j6iyS1aOQyyk+JEVeOIJL93n1qNenFnjzbcdAyARUXnnvae5spxjJpsnpCoosujbJgE89/o877jnNGcnhqmZFqZpsrBW4MLsEjPL6xQrOu97x/2cmRrhmZenAZegBEGgXNNJRNu/eQv103xtdpkfeOgOAEzPnb1hYVMVqR5Z1TdwXO89WZJQ60Rm1734KjWDeCRMNleok119k4b0a+Mfj4i8t32vDtjtQtkoG4/FYj1HUN7vDw8Pdy0Z320WVCKRwDRNlpeXGRsbc19s9qDEUxTFnxbcS/qwW7L2rMS8dN+NTlIBQR0QBqnkazd2ohe0c1yvVqt+usQjok6DEDc2NgYyKbTxugVBQBFF1ks1QqrkS8UjqryV7tMUP7IKyS6RWfVajCQJlHWD2dUi33M7nBpN8OhtJ1hc3+TbV1eIawqWY6MpMrq5JUgoVg0s2+FP//EZhmMhRuJhXptfazrPmmEyFAszkXJrMrbjoMoSpYruN89uQ12YMZ/dQBAE0vEIhmkhCGKT+i+kKOjG1n3n4GBaNqqiIEvuPmzHQREFyrUa0bDq9oRZNqZocvnSJRzHaUq/xuPxpvTrlStXSCaTPdVCvDqKV6uRZblnsYVHUI2ScY/sOqEXufja2pqvyuuXoDwz2d08BRvRz1BUy7L8dN+N3CMVENQu8B6s661Ztxt4KRtPpND4puzVDkKhEMlksillc1jRzs08X9YJyXKD956EYbkJs6im+Gq+eFhtSveJgkClLkVf36zyvXedYqNY5QsvXGQ8FQNcvzy1Jb02FAnhisLr59PmPG3bFSncdeYYL15ZqDf4ipSquq/S23ZtDSKGUkXn5MQwCys5wiGlKcUX1hT0xvvOcSOtaEihWjOwDB1d15FFgfVShRPjGfJFt54ligqnTp3qakHtx+rIU6R5TuNAzxFUYzNr4xiMcLhDarSLOrAgCIyMjLC4uEg+n0eSpD1FUNA5fdgO/XyeXiR1o/v2BQR1QJBleddei4OGtyg4jtNWqND6prxfjuveMa/1Q9NagwJYK9aYSIYp1VN3ofrkWweHsCr7kVUstBVNCYJXj3I9BbObVYZjIT7zzMuAW6qxHQfLNNGUVoLSAHeelNjhxcaybeayG9w0keG1mSXAJahiVUdVOjySQv3EgJVcgWMjSS7MLZOMhbFtN5Kr6q70XNdNNoubmKaFg0OlWiOsKZQqVWLRKIgiqqpSqNQIh1RE2ZWhew4Gu2GvMnPPabxX1Vtruk6SpF0dxrutJzVGZZqm9eVjaVlWkzgikUhgWdY2t4lW9FOrbnSb0HWdVCp1Q5LUjZ3A3CdcL826tm1TqVT8AvbMzAwXL17k8uXLZLNZarWar146deoUZ86c4cSJE4yNjZFMJgmHw/uS0x6U3VG7SHe5UEGRtupEqiJh1J3CQ6rkK/iimoJh2a7XnVOPoOryc9OyMW0b75JEUcC2HWq6SaiVoGLN9kHt1l/LdqjUDGq6wbHRlC902CzXtjXdNlydH0G9NrvMSDJOLr+JokjohoVeLbO2toYsQM0wUBSVeDyG47j1t2Q86k7SDWvu9YkCpmH5hGjZdk9+fHtdDMPhMJIk+U7j3aCTZNxzGG9Xd+1FSevNfSoWi33dv+2IJpVK+T6AO23Xj3RcEARM02R9fZ1KpTLQ3suDQhBBdYF+CeqghArdjP5QFIV0Oj2Q8N8jqGudEmwmKPfvyxtlFEn0R20okugTT0iRqNSbdCOajG66i7QiiXVLIHdPkig2SbBFwVXVVWoGQy2qu6FICNt2kCWxbi20faGzbBtZFnltdpmzx0ZZXsujyRKFSg1Z2jqObTuYpuG+6DhDIAhkV1dZXVvl+x+4HVV2a3+6aTE+NoIjqSRiUQzTarI/KlV1hhNRDNMmpCpuSkkQsGzbb/I1Leua3ydevaZbRV4nUUUoFCKdTvvptMbf6TXakySJSCRCoVDwa2/dolPtajcfwH5nSMEWud2ovn0BQR0Q9hpBOY7jE1FjjahxNHwoFOo4+qNWq3UcB3LQGGQE5R3XAXTTxqiThTdqQ5ZEXyShShIbhitwCKsyuuEu0poi+o29AKosNLk8CII7Zr1Y1VGk5gVzKKJi2nadoNrXoCzLNXF9/pVp3nj6GKoi42CynF1HEkXW19ex62M3JEVGkWS8kU2ZTBoBgXJV59ZTx7AsG8O0iNRnQoU01yjWg+M4lCo1pkZSVHTdtT2qL9qS5MrpJUHArNtBXWs0upZ3o8jrFOHHYjFfjdeaTuvnGUin0z0r8ToRVGP6UJIkEolE07/vpR3Fc065UX37AoLqAv3c4N0u0js1OXpvmP2Mhr8R/fh2Q2ME5Y3aALee5EVQsihg1WtNvvcervuCR2KaLGFaW9SiyjKC4JaA3PQYmKY7U8ndv+gfR1MkSlUDSZL8VKAHy7axTBPDNHBsh+XsKoVyheOjKaaX1zFsG8t2uGlqkny50nTfiYJY9wB0f5bdKHJibJgr81kMa6sJN6Q2j3pxgGKliqbIVGomw/FIXRAhEAu70V4iFj7QCMqp9361znWC7a7le1HkJZNJDMPoaaxGO9i27acgPZLqNvXd6TNsVDBKkkQ0uiWG2cvsNq/u1WiJ5DXB3wgICOoaYbfekk5Njv3iKBJUq7y+1kAgtQayMuqkIUuiPyNKk0XylbrDhSw2OZiHFKlh0q6JiOCn7izb8etGiUiIim66zbj166/pFmvra9i243upWZaNpqokU0muLGS588xxFlY3iEai6IbJSCpGobLlUOFem3sPyaKIadtcmlvh4TvP8NrMIqZpEaovSGFVoVAobm3oOBTLVWTJVQnKsoRl2YiCQDwaxrJthmKRA0/x7TRqo1GRt5NreTd9U146bWNjg6Ghob7O1SPCaDSKaZodp/u2Xs9u8GpcXiTlXWe/NajWbW9E377r/wquAXrt1fCIyLIsZmZmMAzjwBRznXAUCaqpUVcQKNaVe5IgUKn3Bkmi4Kv1XO899zNSZYma4aa5VLk+gqMOTXFngoVVhVLNRKhHRpZtYVo2IjaWZaMKNpuVmts461iIyIiiTSqVQhQarHQQUGQJSRTZLFXQDYt0IooirXV0k/AUgYosYeo2F+ezvPW+824jrmU3RFAKlaZx9e7xLNsmGlLBdvzWiUQkhGFaJKJhV3rfxSLbrzqzdbtWsmmUn09OTraNKLo5dqt5az8veo3nNjQ0hGmabaf7tp5bN8+yLMv+dXrKw377rmA7uTX69kWj0YFM1d5PBATVBdrdlI0ec16NyBMqeEQkyzLDw8MDESp4VkuDwCCHFnqLrO04ZAvV+vnQNE3XqqfvXPfyunOE7EZTgm9zZPn7U+tNvIJjkd/YgPEkm8US+XwB3UgTVhUEUWAsk6RcM0mERaLRCBIOpiU2kRNQT7FtRQ8X55a5aSKDosx3dJPw6lmeiMK2bcpVnVQ9Zeep8UKqTLnamOJzEAVXiTgUDWM5DpIoIQoCsUiIqm4Qj4Zc6b2zuxP/QU7T9eTni4uLHRtcuzm2F6nMzs72vfA3Hmd4eJiVlZW203099EIyqqr6ysOpqak9RVDtPkdPfn716lXOnj3b134PCwKC6gKO47C+vr7N2kdVVUKhENFolOHh4W3WPt7vDcrRfFBj570mwmuN1s/ZU+u5kvEtQ1jT3vp7Rd+yNirXdAxDR5EkcsUKq6urOLiqPsu2iYU1ItEIkigSDocZTqWwbIhoKqIgkIxqFMo6UU1BESVEx+qo4hPr/nsC8MyLl3jDzVOMDkU7ukkIolBvoN5aBLMbm4ykEu4oDdl9Uw4pMuWGURuOA4IoYpgW8aiGZbqu5oIoEA1pzK6sEQ+HKZTKODi7ElS/Tbqt6ER04XDYtwraLa22EyRJIp1Os7y8jGEYXUcS7c5VEARGR0dZWFigUChsEzlA70KHUChEJpNhYWFhT1FpJxiGcegb67tB0AfVBbwHMh6P+8Pwbr75Zo4dO0Ymk/HlqK032SCjmKOY4mtFRTd9p2/TciMhAbBsqFZriILAcnad1dU1JAFym6X6m7A7Lyo9nGYkk3GVf5ZNLBJCUVTXLqhex6roW826yWiIXLGCZTtIkoggCk3uFB4sy0ESBETRjYpMy2azVOHWE6MUq7rvbt4Itz/LaZK7X5xbZiyVwLHxIyi1YdQGuBGUJAjUDINYOIRuWkii4NayLIuNQpl4RMM0bXB2j1AOMoLyEI/HCYfDrKysNIleeoVXR1pYWOj6WehEwF6dLJ/PUyqVtv17P2m6aDTqCzv6ub6dPkPTNG8IoURAUF0inU4Ti8V6MkAdpN3RUSYooe5bV6zqKLjKuI2NHEa56DuZm6bhSrdllXQ67RKKpLgRkiBSsxwE0dXMiYJAzXQH/lH/b8+MtVzVUetpt0RYY71Qxq4TiQRbpq0NMG0bURLqqT/331+5usjx0RSV2vYBhIDfQCw1RFCvXJknEtJwcOo9USDLEpVqcwQliiLVmkEsrFEzTGRJqpvF6uQ2i0RCGqZl+TOydsK1mqabSrkNzBsbG30f17Ztf6bY4uJiVySwk1LQM0FeXV3dlp3ot44UjUaRZbmnhmUPO6UG96IMPEwICKpLXC9uEh6OCkHZtk21WmVjY4Pl5WV0XWdtbQ0BgY1CkbDiqt7i8TjHxkf8iGY8k3RHXShyg7WRW4OS6oMLwe2PsutuDJpHDsJWZFSu6kiS2ycV0RTWimWsulu40CIz9+Cp6ERxy2liPpvDsmxGk7FtbhJe/cl2nKZGXt2wqOg6YVVBUyVCiuJL3304bg1qs1wjFtYoVw3kev9TuaqztrFJSFUw6vfKQURQ7Rbe3QjHEzuUSiXf2aFXgvLIJh6PE41GWV5e3pUEdiMaT+SwtLSEYRhdb9cJpmkSCoV2dZvotG0nggoiqAC7IiCo/UOjjdPS0hLT09NcvHiRK1eusLq6imEYhMNhZFlmZGQEQQBRDZFOxjEtB0mSiWiyO3bDgVh9DLp/zsKW954oCL6oIqIprjLTtAjV02gi+Ns6gG3D5EiKqmFiWTaW5UZQgkD7FJ/jEpQkbkViFd0kW/fYk1uaf6V6KrA1xefgsLZRJBoJoUiSaxRrNN9vbg1KoFCuEAlplGo6ougSaqlaJbuxiSJLbc+zHa5VBAVbabW1tTVfOt3vMVKpFKIosra2tuM23RCNJ3LUMuMAACAASURBVOZoTB326wbhbZfJZDBNk1wu1/W2R4GgApFEl7jeIqh+HNj3C3shqN1snHYSpQCsrKy4/VC45BBWZX8WVLT+dwenyRzWG7Vh2g5aPT3oiSci9QGHNWOrGdZ1rGhuwB0bTlCuugRnejUoBKx2IgnLRhBcpwkvq1aq6lxdWmNiJOX+vOXzxMG3UGrEpfllHrrjrPv5qPJ2gsJBFERym+U6gVnuNGFJolSuYVpuClSVJXDYNc3XTwTlSZ9b99NNxOEZws7NzfU1pbbRVaHRsbxTj1S35xUOh5vslfYSQXnjanZym+i0bScSGtQsuv1GQFBd4nojqEGiG4JqZ+PUOvgwGo22tXHaDY7juRdARJF8o9iQtkVWkYa/N47a8GpOnl1QWJUxbZuqYRGNuouBGxltXZ9lO4wMRSnWCcpLxYmCgG1tX/BNy027SZLo04FpWdi2zVq+xGgqTioWJlcf/e7NjHIcp2kRdBx46fI8b7nnVhzHcVN1ZmsE5dbS1vLFLWNYy7ViKpTK/rE9YcZu7zT91oLa/azbiENRFJLJJOvr6z0RQWuU1kgCsiw3uTl46GX/nr3S0tLSnmZINTbadnKbaAfTNIlEItt+7rS5V65XBAR1gBi0WAD6b6zcCyRJ8q+73eBDrzbg2TjF43Eymcy+eAcKgmta54ohHELK1rDCcJ2sHFxXiFqduBqjKQSXoLzxHO4EXsdVBCbD9WO4gw096KZJKpZks+IWzi3LQpbEbb/nwbItBFGoO1Js/btt23zr8jzfe+950omoT1CS4H6PrTUoB4dyVccwXVfysKZS25bic1V8uc0ykigiSW79TBQENur71w2TkKaCsLtarpcIyu9Js+1tkUmvRCfLMuFw2O8d6uYc2kVDntDBI6nWKMOyrJ5SY8lkEtM0/TlSvaI1CurkNtFp23Yk7z3zN4JpbEBQXaKfL3vQN4hHFAf9JuUZ23rRULVapVwuc/HixaYJvIlEgpGRkQO1YBEEwY1cbJeItMYIyiMrx/HNYWFr1Aa4ZCAIW429miJjWBblmuEPJxQQcBpSfDXdIBkNMbeWBdwUnyyJLlFa219QTMubvURTyGI7DsvrBUzLIhnfcpOQ6j1TrQTlXi8UylUyQzESYZVag1Es9d1796Fl2yQiYUzTgrqs3jv/kOopvnYXSbQSSyOpeW/v3h9wF/3W+7Cfce/hcBjHcXZ1dfDQSZHX6ObQ6lrRTySUTqfZ2NhgY2NjV8PbdufY+jy0c5votG27c91L4+9hw41xFdcA/ZLNoIb3wZZQYr8IqnEUfGNqzkvXeESUTCYpl8ucOXNmX47bC7w3R8/sVZVFSvXGVUUWKdVMHFyy8iIob9QGQDSk0KgXCKsuwZVrJorkSrlb6zTlmkE0pLK+6abMXK89r+eqXYqvruITxKYIyrRsd/R7VafxEJ7NkWPbPlkBft/S9NIamaEYsYi2Tf7sgN8UbJo2iWgIvV7YL9QjqHK1RkhV6ka0OzfpehGUbdvbiKgR3vcgCAKKoqDrelPDbD8EJUkS8Xjcdz/v5OrQuk07dHKt6Od5EQQBWZYplUrIskw8Hu96204Nvq1uE50ipXafYUBQAbqGV4caRE9Cv0q+Vod1j4y8UfBeam4nY9tBRY/ecY16ilGRtoYSKpLoj3hXZYlSyV3MG6OpWKhZ3efOjDIp1gwkSUAUttdpSlUDVZFY2/RqOjaS1Pn7dkUSW4MPPZiWhaq4irpYeCv1JIgCtuOmC5s/awcEeOnyAvfccoJkLMLMZnMTqeNspeR00yQRCVFtcJoAKJQqTI4Mg7BV79ravjkiEkXRn5XUSEI7fd+e64qu6z4B9Cq28Kbptrqf70QGu70Yeq4VjWPZ+yEoj2y91KE3U6ob7HS8RreJVuun3VwkbgQFHwQE1TX6XXAPM0F5RNQYDbVzWE+n0wdqbLuf8B72RkPYmlEnK1FEt1wVmyJvzYhqHLUR0eSmURuaIlOolNms6O6UXLbPeIqG3CGA3igM07ZRJLGj4MC0bQTcPqhGMqjpFpqmohsmschW7UGqR1C27TTNpfKwWa7iOA5DsRCVFvJx6tOBAWqGSSyskSuWvX8FIFcocWpq1D0nAWpthD2+wWwiQblcJpfLkclk2l9gG4iiiKIoviKznwiqk/t5OLzdXLdbxONxDMPw04b9pMQ9kvEUh/Pz84yPj3etottpbYlGo1iW1USijcdshxtFwQcBQfWEfqTbh6EXqnHUh0dGuq5fc4f1awF/hIFHUJLoCwckSfAbWRVJpKY3j9oAiCjylmAC6vOdzK1pu4q4LQuWjkewbIdkJMRyvohpWttqRY2wvGGEotgUQXnGrS6RNBfO3REeTlOKz3ELTO712jYhRaFSba5B2Y7jE1SlphMNaz7FOo6NY0M2V/BnXtFFRDQ2Nsbs7GxHX7pO8CIn0zR7JqjWepJHBgsLC23dz3t5TlOplG8G2086vrGOJMsy4+PjLC0t7TrssNtzTCQSWJbF0tKSP4xxNxeJgKCOIPohqGvpx9c46qNWq1EoFLAsi2w26xNRKBQikUigquqBE9Egam+aprmRoSd6aBhWKImiq+Jz6k7mZvOoDXDdwI0GglJlkVJdeGDbDpE2qZNUPIJt2ySiGsv5IkZdxt3pVjHqKT5JbJZgl2uGP55+NLl1HEkAx3awHNehwkPj/h3f2aKGVyVztv4H27bYLFdJRMPu8EMEQopKRddZ2cij+AKQ3bMFgiAwNTXFzMwMmqYRDoe7VqtKkkS1WsU0zZ6epXaEpiiK3zB77NixvlWCjWaw/aTEW+tImqYxMjLiRz2dIp1e0ompVIpsNusPY9ytSfdGsDmCgKAOHLIsN1mi7AcaiagxImoc9eGJFWzbZnR0dF+P3w284YHXmqAUxRU5eOIEURQaRm24Y+BFUURudDJvGFwYUsQmglIkkc2yG11ZjkNElbctrMlofa5SxH1rdVV8Uke5gWW7wwFdz7+tBbGiG24PVs1AUxRfsuClAr0UX6tIw3Jsv262Wak01dBsxzM7FskXK0ykk65oQgBNVajoOrpuuvuWmiO6VoiiWG+CFpAVhfPnb8Wy3ZHzqqpi6FvpxdaXJa/h2kv1JZP/P3tvEiNJfp53/2KPyH2rfevqvXuaPT09G0VqtFG0Fn4WBAgy/EG66SBDB511MSwYgi3CgG+GBBi2Yfukgz/4IhiQKNjaSNHcmuQMp2eml6qurr1yz4x9+Q7/yKisrbuqmpwhR/0Cg6nOqsiIzIz8P//3fZ/3eSpEqUniaYDkpIzLsqxMa+9wCewsG7DRjNSjR4+wbfvUPaTRuQ4DTS6Xy1TZT6LFn5XMMDJjbLfbGTHjuPi0qEjAS4A6U5x3WNdxnHOdb9xzagRG46oKo91rpVI5Vk293+8fq7z8ccRoBuzjLhdqmgZJkpXpFGnfakORJfwoxpBF/8c9AFDiZ0Pbz6ZA2HD0U/HVOBbDsIeX8ErepDuwKedH5UWhGH5ShhBGSdaDig5lHqOB3DCOsQyNoesjSzJhHB1g0AHIioxj22iqUJDImQa26yNJB2elRiW+dm+IpWsokuiWjcRvs2tW5IwII46V0kxP2NdHUcxub0jf8Ri6AUPXp9cf0G53+NnXb1LO6Wysrx+5R0eL9ficWxzHBEFwaiB5nvp5EARsb28zNTV1rh7XKEzTZHd390w9pJNkjorFYjbIOyrNHT7uLP2u8UFjSZKOVcMYMS1fZlD/CONHpSbxPHmf8S/5WdXUP016fKc6b5q5hKMMSpJwxswK/ZTKrYxlUMqYs66myJkihCyLBXo0tBvFMaauHAGVvKXzZHOHuekJAILn9KCCMBILv5QC1BiOjQaMwyimYJn0bRdFBs8XWZIgSYgMyLIswiDAcRy81LJhRJcfRRLvZ7F7qZqEnD6HoWsosni//DDC0DXiJCZKJDpDl77jYbs+Q1cQRN68Os9Ou8fDNeGxFIZhmgFJ/O133udXPvcaC4uLJKdg6I0yqXFm37PieSW78T5SrVY7FxtvBDS1Wu1UPaTx404Cs1FprtlsHiGVnIcOPlKbePz48bFKE6NN0Sc9g/nDipcA9SOOcYA6rbzPSTpzZ41PyjhwdO5PREUjzR6CKEFmf+h2pLcnvr9JClz7ADUSilXHLOFzhnpwTilOMA/5LYGgqd9f3eT6xXnxd9HxpbjRvzJZJVmQNuJ4/zPKxEfjmGLOYKslZ2QKUYaTDszSFosl2u02A8djoiIklMardEmSpAoSAnhlWRK+WJJgKA79EC8IGToexZxJEic82Wnx4do2gR8QhgFBIIBIikPeuHGBoe0x8ELKhRz1kkU5Z6KrMqahC++sNDN6Xowz+4AzA8p4jPpII/r5aUuH4zHK5sZ7SCc5+x4+7llAMyrNdTodKpXKgePOk+mMaPudTgfTNA+oTYyA+SVA/SOM037o4/I+ruviOA4PHjz4kcn7nBSfNkXzU513NAcVReRMNVusC5ZGFCdIgCKl4rCZ9ft+lqUoMn76eF7XDgzahlEsFvUxS/W8pZMAj9d3sHQVWZIIwkCw7VLx1ZEu4DheJYChKKLfJehz2Tmk9A9KKdVcliTCWGRQmnboKytBuVwmCCJAolTI0Ru6kCpqJOnf2F6IF0aEUSxkjQBNU3m63SKKI9q9AdP1MlGSMN+o8P7j9YzZOQKiUs4kihPevLmMks5LuX5I3/HodB229p6iyApv3byQlZqeF4qiZOMO5wGVA29FSj9fX18nl8udmy4OoodUqVRO5ez7vGxtfHZLVVUKhQKwb7VxnojjOLP9GFeb+DQRJOAlQJ0pxm/Sw/I+o/9GN+soIyqXywyHw09EVWFcE+/jjk8MoFKbiyBMKBhaVo7LG/v0cVOXDwCPLEnYXrqLl/ap6DldPfB3fijKg/sPJTRKOYIwIopjXD+kYGp4fphRwzOx2BSDRrdQkiSompJKIe3fV14YiiwIKKY9LVkWGVUcizKXPE4DlyRURU3PF1Mt5uk7HlutAV6QZkduwNq2EFoNwhDTEBmGripEcYSiqHSGLiAWvpxp8Cs/dRsgK1U6Xkjf9Xmy06GctyhaGl97/8mB9z6KJXY2t9B1jTuX5wjSUYbnhaqqmUqJqqpHQOosbD9FUZiZmeHJkyfnkh0aB5pSqUQQBOzu7qYWLseD1GnKiSONvZEQrGVZ57boGIVhGEfUJl4C1D/iSJKE9fX1TN5nJOY4AiLDMI694T4pRttPquXGi55XQswFjQ/d5g0t1cADU90HK2PMakMcL2VqE5YhlMxH76EfCqWHJBmpmSdUCxauF6BpKgPbpZQ32Wr1UYQmEtIJCUGSCKZfeEirz/NDITIbCd28ESDFiSjdCTdcFS8MGdg+figyoyAdQC5ZOmEUU7I0PtxtpnNwsQAiVcH1Q/QUEBRZ5ubSLIkESVpmjBNhLaKpMlutPivb7UxsdxRP9zq8fmWeO5dmufdwI3tckWWW5meR4hA/iNB1A99zT/W5jc9IHQapswrLappGoVDIbDXOon5++G9rtRrb29vP1Nk77Xd7fHZrZmbmRJmj01zn6HyH1SZeAtQ/4pBl+ZnyPifFqNT2adHHOk18Uv2v0RxrEMbkxmaacrqKH8XIEhhjVPJxqw1S1QU/jkjiBENVCMI4A1o3CCkYKvu1OolKwWLgehSLRXpDh6Kl8zSKhVvuM64zThI0RSaMIlGWTIdkXT9CTlXQizkDxxelr93uENvzMU2drXafqUqBZqeH4/lEcSzIEECtXODB2jbXL8xwaX5GeAvlLa4sTKMqYtNgaKKslogXzHa7z/urW3zu9lWCMCaMfB5s9LmxOMFGs3cEoJIEPny6y51Ls7x1dZ44AV1TsmzL9gJafRvL0ClaGuEpxizG+1GHmX1npYwDmerFWdTPj+sJHS7PnUVn77jQNI3p6enMgv48Jc3Da8lIbWJ9fT0jVH1a4h/PivlDinw+f241iU8CoD4psdpPKoOK09caJwk5XcmAaCT6iiRhaAJ4hLOuyKzi1MhQliU8PyJOBGPPDyOhroAwMazljfT9FOer5E1a3QGSJDN0fYqmThhFHGo5ASBJIrtDEmrosiwhqyphGItynB/S6tu8eWMpHfw1ebLd4s1L02zudYSGXpKwvdfG0BQuzU/ycGMPXdPFc8kSxZzF1YVpJCTKBTMVpYWB6+MFEX3HQ9cEVV4CCpaBs9XiyY5wco3jGE1V2e0OyO/o3Lk0y8p2i1LOxDJ0jDEgcvwQy9DoDFwebbUYOF4GZoPBAM/z+OLbtzE1legUw+rjzL4XEZYdHVMul5Fl+QD9/FlxUqluvLd1WFrpPAaOIxLG+vr6ub6bx2VepVKJb3zjG/yv//W/+PKXv3ym5/txjp9cTZtPKH7SjAs/sUzmEwAoWRa9pTgW/DlT3VcpF/NNwmpDU2W8MCKKI6wxENNkJVMglyQJS9fwwyjrELl+iHagBwWlnMFOuw9Ad+hSL+WwbXsfgGQFRVVRVY0YQcZoD10hQSTLPN5s8Xizydp2i829Nhs7rVQpXPR/psoFAYayIkg2usbF+Slyho4sSVyZm+DCVCUb6s2ZOj3H5QeP19lq91NVjYhO38FxfYaOUC5PkgQvjMkZOrWihev6osclSZiGxk/dWGJxsoyqyFycrkOaxd1f2+Mf7q/xN99/zDc+WOP9J7tUCiZBGB7ItAqFApIs83f3PgBJPnXFYcRQg31G43kAapR1VSoVJEk6lZX6s3pJo97Wzs4O/thA8nndAkzTRFXVLJM6S5y02f3CF75AqVTiT//0T898PT+u8TKD+hjix0GP7+PO3j5OgBr/gkdxTCzJxIko5XlBKOwvFEVIFkmgKwq2HyJJMnlDyzKrUl6U+0ZPJ5TM98tTQy9EU+RMY0iWJExdY6vdR5IVekOXct4kVygSp0aBjh+x1xsQhoKFF8UxUSSuSZZl5hol7j/eyMRGNU30kDRVwfFCLi5MIgEXZ+oYmoqmCqAauj7tMGKyUqBveyQkRFGMqWvkdB1V11nf3iWMBAiNwvF8DF3LRGRNXaFSsKgWckRxjCSL7O7D9SYDzyMIIt64Oo8qSVmWNR6jTOvVi7N858E6pbxJOW+SN3V0dRFVUQSbMB0CPs098aLCsrAPauMyRv1+/5kluueBzXh5biStdN7v1sgY0bKsU/tbjeJZ1Zjf/u3f5r/+1//K//gf/4Pf+I3fOPN1/bjFS4A6Y5wng/o49fiOO/enJYN6njGeoqTZTUpsEEKvAbIMuibTtmNkJDRFzuw1LEPN7DiKpk4Y7z+fqSm0+k4mnmr7+wO4mqqhq2LxfbzVwg8jukOHX377JivbrXRoNiJvamzsuAwcD1mWMyAaibhqisorF+cJkwRNST2iYtGfsr2AXKpc8WS3y7VFlyhK2Gr1svdhfa/LQqMsiCFRjK5rVAomm22VmYlaulBLLM/UkIAgEO67SZLgBCGaqtLqOdRKwsgwSfnwzTHbjnuPNnnr6jzL01Ueb7XRVJl6MUc5b5E3dQxNRZYlXr86jxdEDFyfvZ7NwPHpD11Wn65z5cICr12ZJ/C9U2UM46SJF7HAgNOrn58GCA3DyEgJc3NzL2z1PhowbrVa1Ov1Ux37LKt3WZb5t//239LpdM58TT+O8RKgPoZQVfWIkdzHFT+JAPU8IBqPw55EUSScdKMoTr2gxPuuKaLEJ6R7pEwo1tLUTEy2mFq/J5IozRmaghskSJKME4RstgeosoztBzzYbHJtrkEQReiqwtPtJlEsmHR6KngexzF73SGXF6bZ69mYuoquqgLkUsHaKIlRVZnQD9nrOrhBxKuXxEBtz/EwdZWEhOlqgShKMvPBUYRxTM/xxWuOY0xdp1HOsRzUCMOYBEn8P0lw/IDO0EFTFcIwojtwmSrnxGOaTBBFyJKcLdKqLFMrWVQKFkEYMd+oMN+opH26kIHr0+o7DF2fgetza2kKPwx5b2XrwDU2Gg0+fPyEYt7k0kydwD/dd0HTtGxG6jxkgvHN5MivacSgO0mr7jQb0Hw+n0kY5fP5c1u9jwZqRxneiHV4mmOPy6BGADuin38a4iVAnTF+0npQP84AdV4gOiliBEkiihNhjy6RgY+qjEBJQlEk/CBCVmRMXaXnCJq4lRIm/CBkpztEVWQ2On0kWWJjt53uUCVc16fb7dG4Ps/Q8ShYBjMTVfquz8D1uH1pniRJKFgm9XIeWZKYKOex/QDbC/CDkDCOQYIn2x0sU2emViDoRYRhhOuLQd+e7VEt5BgOB8iSnBEU5huiNyRLUlaSGxd5LZgmDzYeA8KkUJIkVrZaXJytQ2pgKKWzX2qaBTpeQKc/pFzII8sS79xaFkCUzlFtd4dIksR8vcT//WANxzvKzLv3aIO3ri1waabOw81meh/ATKPM1fkGOSO1pNB0wsA/cvzoPjhslum6LrVa7VylvvHQNC2bGzqsfn7WEMPRAb1e71SgcjjGS4OHSRjHSRiNx0kAFQTBp44p/Ol6NR9DvASo08U4QP2wgejkEOy9IBK9FEWRcf0QRVFRZRk/TGV/JJmBF9IdesKgL4ho9myiqIIfxgwdj51mB02R+fDJFrqZ58J0nQfruySArmnMTTdYnmngBiFxkjBRLjBRkXBcn2rBymarHm80Gdo2N5bnSOKEVlo6i+J436fJ9en0HWZrZZ7sdsQ1S8ImZLKcZzgcoKZuvoosYXuhmH8KQoIwolowBZsMIdNUypsZaSKOE1RVodfvs93SuTpXJ4piVFVhqlYkSRKuzE/geQF7nT7VkgDUb3y0juP6R5iIiixx99IsX7u/yvj+Q0bMYHUGDvONEpOVfCax5IcRthvQGdg82V7j8sIUlqrius4RDcrDHmXFYjFzBDgt3fxZJUTTNKnX60fo5+dh49XrdVZXV3Ec50y+WHBUcfzwIO+zFCZOAuoXVTGP45g//MM/5IMPPkDXdf7oj/6IpaWl7Pf/6T/9J/78z/8cSZL4F//iX/DFL37x3Oc6bbwEqI8hPknRVkVRPrby4vjCMLLPPsn358WA6OhzjRriIMpeIKGpCn03wAtiFFlivdWjYOjIEmw0u2zstZEl0eivF3NiVioUFHHTNFAVGcW0SEjQVY3ri1PEcUI5b9Eo5akVLfa6Q3a7NoamUM4bNHtDLF3NOOaJBJIs83hzl8vzU5RzJl3bFSw/RaZRzmeZkSTB0mSFKGUA7vVsLk6ViZOYhxstlqZqyLLMwHEPMOYsXSeKRO9IDBOrTFULhFGCrspYhs6rVy8gy8IkMYyijIRhqTJ922Wj2ePW0EVLy06VnIntHs1yHq3vUS1YfPb6EkPXx9RVNEVBUWSCMGbo+Wx3bSbLOe6v7bLTEQaOQeDjBwGDwYCHqxt86Z3XsG0bz/MyDcpneZRJknRqYdnnueIWCoUj6ufn6SWNxJxd12UwGGQSRqeJ4/pII6bgSF7pWQO3J9l3vMiQ7le+8hV83+fP/uzPuHfvHn/8x3/Mn/zJnwDQ6/X47//9v/MXf/EXOI7Dr//6r78EqB/HOM+C+kkqOvwoMqjTZESj+Y7RF/eHDUQJ4mdFFkw9VROLSxBGeEGE6wvJoPVmj/srm8jyNWH6F0XIskRn6KRlM5WhF2F7AY1yDi+MKeUtbi5Nizkhw8API9pDh3LeFOSHKGRlu03B0vn2h2sMHJeBI+wrHD+gXhRNeCFJBI1KCVVOCKOIejlPvZwjIUGVZHRNwQlCfDvCD0NmakU6gyESEo+3W/zC7QuMBM8dPyAB5hplVrbbkCSYhka1YAqlc0XG9nw0TWW2VhbuvpFgzq03u9iOzyuLk3h+iGWIea0gFDbwAAPHzXysLs/VSUgwdZWiZQogUgWQjvQCc4bG4+0OA8dj6PiEUYgfBAR+wI3lWa7M1vnBh4+JkgRN19A1jXqtTq/X44OnO7x2eZEg8H/owrKnybQOkxPOY/UOAgynpqbY3t5GVdVTa+udBIi6rjM1NXWsCePofCe9tjAMn1sefFZ861vf4p133gHgzp07vPvuu9nvLMtidnYWx3FwHOdjm6t8CVBnjBf5YD6JgdkXAagXLc3Nzs7y5MkTTNM8087uOCBSFaFt1+479GwP2xM2ELYbEEYRV+YbLE1WCaIIP4jxA9HH6TsekiQjS6BqGnlLzA9VikWuaha6qmAagommKTJDL8T2AvqOSxQnrIxRqz0/IE4SzBQMC6bOypbotUhAb+jQG7osTgk2Vs7UuDTTIIpj/CCiN3AxdI38iIwBbOz1Drz2jb0+pQUTSYL+0MPSVaIkwTLUlDUozrU8VUWSJeFRZWgE6Wfc6TvomoppKDS7Q7xAmBH6foRlivJPZ2hTKeaoFXPYjkPRMqgVLFRZgI+pKsTAlbkGQzegZ3vsdocpGcIjCEJ0ReZzty4Sei4PVtaII7HAj4Do0UaTajHPl37mdTabPUo5A8sQzEdVUYiSmIHrkTf0dO7rbMy+ZwnLnhZsRorlvV7vWA3A08SILv4s+/mTjjupXzQqQ46YguPX9Twn3Rcp8R3OAkfs49H5ZmZm+NKXvkQURfzu7/7uuc9zlngJUOeI81q/n3eX9iJxGsHYH1WPSFXVbDe4uLh45JgDQCQJivUoI+p7Pn3bYzjyI1IUXrs0w6ONHTb3ugRBQBD4qQWFgpQEzDcq5E2Djj1A1TQUWaJWLmPlCqm9RsyEKsz32gOXruOjyBIr220e7/SQWCZIZYryupKWCvdj4PnESULeMpitFVEUGVmWuDhTQ5Jkojhmu93nczkDJGHt/nCzmb2PURQxHNrcWJ4Xc0jy0fdwBKogcXG6Shgn5AyN6VpJWLVLovRXLVp4bsBWq0+tMJdJIjV7Q+YbZUxNY7ZRAhKk9DyVnJku8KlorqHjeR6lvEnONPDCMBPXvf9kh0alQMHQ+Pb9x1mJLo5iZEVG1zS++cEqb15fwk+ZgrWiJebAvyVTDQAAIABJREFUDB1NVdJyISxNVdntDtlsDRg4HgPXw/UCdnZ2uPvKFa7MNvDPwOwbvZfAsaBy2l7VOP38vGy8EbVbluVnZj6H43mEj0KhQBRFmVp5Vr5+BkCNwPK8USgUDhicxnGcnetv/uZv2NnZ4a/+6q8A+J3f+R3u3r3L7du3z32+08RLgDpHnAegRkSJTwKgRgSN8wDR6OfzRj6fJwgCbNsWFvSpBbkiy3ihUMgeAdHFmTrtvs13H20ShKJUNA5EugyvXVmk2fuBaKJrGrVyjmrBolbM4YcxqiIsybWU5da23cwj6Tv3V1j8qRtIwNOmUH+QJYm+I3otmioLxXJFoV7MEcUJ9WIOQ1NRFQVVkYhjMei7PF0jDCPaAxfPD0TvKklQZIn/9wuvE4SpHt/Yeyua3wYP1raIk1voqsJMrYimKiiyjKxAHAkChSRBuWDiBxGaovB4s0XJMiCBnu1i+wGLjTLlvImlK7ieyCp22n2uzE1gGSoSYGoqpqZyabZOzhADut1Uudz1Axw/oJK3WNnco5SWMAHs4YD/89FjfvXzr/H2zWW+9dEaZU0jbxnUijkqeSF9FMcJry7PIklC8Xzg+my1BwwckW1JwFvXFgjCkKd7+7M5qqpQq9W49/4DijmTyXL+RGbf4XiWsCycPoOCffr52tramYkOh+NZmc95YsQUHFdT/1FmUHfv3uV//+//za/+6q9y7949rl69euBaTNPMnLuLxSK9Xu8Zz/bDiZcA9THFCKBOayP9InEYcE5DVhj9/CJxbI9IkampGs1Oj87Qo1Kw+M7DDYaOTxRHWc8iCAJWN7b4pbdvU9AlNvoOeqpKrWsqtXKecsFCAn7x9ZuA8G4K08Z8FCd4YYipK2PaerDdHrBYzxPFMVY+hywJCvpsrchGq48iS3iR2P3rqkIcCZmkibIAKNPQ8IOIgePjhxFRKrJaLVi4fkhv6Bx8r+MExwswdRVL1zA0jbypYmgamipnLMKRdYaiyHSGLn4Q4YfBAWZcTtcIY6EOAalXVLaTjmj2bRqlHFamDCH8pyxTR1UUHD8kSj/zle0WixMV/DDi8dYur19bZGDbPN3pMHW1QBSFwpU3Pfdko06hWMTxQyYqBX7x9esosoSEMHccuD673SEDx2OqWqCSt/jGh2vH3hf3Hm9y99IsfcdjpzPcn6/KN7D0JUxdQ1Fk4MWFZeHs4rKappHP5+n1elSr1TOpnx/+zhQKBcIwZHt7+1ib95OOOynq9Trb29uZU/BJADXaaL7IBviLX/wif//3f88//+f/nCRJ+Df/5t/wX/7Lf2FxcZEvfOELfPWrX+Wf/bN/hizL3L17l89//vPnPtdp4yVAnSN+XKjmp82IDMM4MAT4owIiPwhRVYVmz2anM8D2AoauaII7rku33eGf/txbLDaK/NX/ffdAz6JQKKBqKhvNHm/dvETXdjE00XdR0sa87QZstgdMVvL0bY/3Vrczx9sbCxO4EeSNHH4UU84bmUp5OWcQRDEFy6CUMwijBMvQuDHfIAEapQJBGKHIEn4U0Rk4zFZzBFHM+l73wGuP4gRNVbB0FTcIyJk6tuujayp5Q8PUVWzXJ2doKLLMQqOEH0W4foQz9FKPpii1wUjQVQXH8zOLj+zzRPS44jghb5mU84bon8kSy1M1RutvGIvMb6dnI0kS3/7wKV/67GcIwwjPDxjYrlCskBNUGfwgYHNXvKacafJwfZu3ri9yY3mOSmGfVTbfKOMGIiNa2+sx3yjxYKPJRvPorrndt7l7ZZ67l+f49oP17HFZhlohn2r1RVybn+Da/CSyLObQhq5Pz/F5vLlHb+jw2VuXTt0zPUlYFg6Wpk4bsixTLpfPlP2cRHSoVCoEQXCszTuczep9pKY+6pWdZHI46m+/yHdblmX+9b/+1wceu3TpUvbz7//+7/P7v//7537+88RLgPqY4kUA6kVLc9PT06yurpLL5c5UAjgJiOI4oTt0RWnO8xi6AbbnE4YRS1M1liYr/N29D/B870Dz3MpZ/J9vvseXfvo1fuaNW0RxTMkyMHTtAEPMDyNKOYMHGy36roedCpmOYrPd5/XLs1QKJq2+yGB0TWW7bzNXzeOHEaaqEMUJC5MVLkwJ6vZsvUzOEFlJe+BwZUY8/mirBYiekB9F+JGwvPDDiOlqka1UDBZE+c3SNQqmTnfgMl0tZsrmQapK3rNdJioFwigmShKGjk+zbx/6TMWMUtd2BStvq42iQN40MjHXRjknVNlNnVopn4rYwnZnkLrjRsRRxO2lCcIgQkLi6dauMNOME2pFiyhJiOKY2Yka1aKFJMnoaUY2WS3xmcuLwqlXkYnHvKma/SHvrmxn/3b8gMszdVp9G9c/eB9LwJOdNjcWJ/mp64vEJGPU80gM+naGGKpCvZTj799bPeCDlSSw2+zw1Xcf8jOvXjmXZt84WERRdOZKRRRFlEolFEV5ZvZz+JiTMpZGo8Hm5uYRm/fnHXdcjPfKgCPPB2cDvZ+k+PS9oo8hzptB2bb9zL/5UfWIRvMVGxsbLC0tPZOsgCQhpWQFPwwZuMEBIJJlidcuzfJwfYfNvQ5hGGTNc0VR6Ha71Eu3+LnXb/DtB+vUiqJHVMqJhVdNiQWz9RKuF9Ieuux07ZQM4WWL8FvXFqkWTDZbR3fsQ8fj4WaLV5ameLLToWgZFEyDKLFTw0IJXRNgl8QQhzGOH/Jos8nPXp3AD2NW1re5MlMhjGJkhAqFIkkpLVu48Q7dgIJpsDSpIksgSzJBlGCmqhPfffA0NQBUWNluZde31x1yeW4CWZLYbPWZq5ew/SBTX1BkYZKoqQp62isTRAtBrPADkV0VTJ0gjLAMHRnY6/QAiZ1mOyMzqCnpQ5AkoFIpEUQRhq4yVS2RN41MLcIydMI4ptkbEqfSRw82mlyeqTFwXHRNZH3AAYFZgM1mj4JpcPfyHJutHkVLfJ7ZxiKM6dkepZxBs+ewsrOD4/pZhjuK28szvH55jq9/sF8OlCSxoLvDPjutPjP1Er7vn9oyHjhgGf+i6ue+759KG+9ZTDxJkpienmZ9fT0rIY7iPGAyGuR9/PjxsRnmp82ocBQvAeoc8aKCsZ8EWcGyLCqVCsPhkFqtlg2DKrLwPBqmrLmB63NxpsZeb8h7K1sEQZgRFUZAZCgSd67Ms9fuo+s6ZV07BEQKuqryC3cuE0WxoG27Prs9h4Hjsbq2zhu3rjBdLfLR+u6Ra00S+O7jTd66Ms9UpUDf8aiVcpRzxgGGGBIsTgqGWJwkbHeGyEt1nCDESu01DE0hZ6q4qeSRrgl7jXw+j+/aBFHM/GQZRRIGg5IkUS/lKeUMeo7P0PPJ6Rp7vSED1ycMF9EVmbyp8cHaDputHouTVaZqRbZbItPa7Q4AAR6qIjTuZmsloR6ROuQmqVis7Qc0e0PmGlW6tsNOa0AUR6K0Z+rs9mxKlkmrN+TSbANZAssyURSFnCGEYUcZkyRJXJyuE4TCeC9naLi+UE5/sNEUPaggpNWziWNBBgGRKeYMnSc7zbQXJMgVS5PVbGMxMiRMEphvVNhqD9jt2gxSC48RENVLeV5ZmuTJTusIOAG8u7LFW9cWeP3KPI7nkzP0A2aHQ9enNXCo5E38Uw6YHyZNnIctO57VjNPPn0WceF4mdJI6xHkFZlVVRVVVdnZ2jtDZD5c5Py3xEqB+hHGYwRUEwSdEVpBQFIW6qtPs9ui7AXlD4zsPN3G8gCCKDjDm1rd2+cKbN7mfBHRtG03TyeXylHWNasGiYFnIkswX37pBgoSqCIq17YUMHI+9niMkdObq3Hu4weCQIkGpXOHvv/0e//Rn3+QzF6b5fiouaukq9VKOUk5QleMk4er8RMYQ6x9iiEVxzNvXFtOmM/QcT4BMIjIoNxBEglphBi8QZUMzNSu8PNfg6sIEQRijqyrV3EiNQQCMKktstgdstnqZakTXdgnimKKlZ1lTkiRstnosTJRRGmVkIEr7STlDo1HK44chUQy6KrO22yUIQn7+9gWiJGFrr4Pv+Tiux5XFaTrdAQM/IopjDE1DkcQAsJzOgUmSJLKzdAZKUxSiZB8UE5IUMMDUVfwgLcclqR5hEDJTKwlWpKqgayphFNOoFPHDMFOaUBWFRjlP3/FojgRhHRcJiTevL6BIHJvdNntDVne6J9hvqGjqKMMFTZFZb/UYOALk/DDC80T28s7rrzBVKZya2TcSlh2pn581gxp3tz2sfn6SQ+1pMqHj1CFO6iOd9honJyczqaYR0IVheKJK+09yvASoc8RhADlNRjSSU3EcJ7uRflRAFIYRiiKz1e7TGbgMXT8DItdx6fe6/PrPv00tp/H1R6vZXMsIiGRNZbPV551Xr9MZugdUuKNEsNS2OwMmynnafYcPnu5mJafxsHSN2xdn+OoPVg88XsgZzFy9yMB2mKyU+PzNpWzn7vghA8dnuztg6PhMVQuUc+aJDLHvPt7kjStzJAmEkcgkZAXyhkYUJ1TyJoYqsqlaIYeuKHR9wUCLojp9x2Nlq8nyrSWCSKidB2GEqSnpPBLs9YaYusZcvUwQCoAKo5i5RhlFFvNbYRxj6SoDx+fRVjMzHXy02SRKe0VXFqepWBoPWm2SRDDiZFkhl88zsG06A4elmQkcPyRJhNBrKW+iyHImkSQhlMQ32z2SBBYnyoRRRHcorrVr+2kPz6TVEXNekiyhqTKaqmC7AZYhFvNK0WKhUSZISSPtgYsiSzR7No1yge989JSjn2rCvUebvHl5jp7jsdHsZay8aiFH3tSeab8xcD08P6SUs7hzaRrHDWiP9ecMQ6dYKvK1797ni2/fJmeczo0XyLKn0SDvi8Qo+1lfXz9R/fy0vS5d1w+Ayot4SCmKgmVZVKvVDPRGpqQvM6iXAQiWkOd5qKp6ptLcKN2/cOHCmXZ4h4FISjXV4jhh4Hj0UqmZoetjp0D0ytI0JcvgH773IUGQ7ipTIFI1nb+79wG/8OZNQiR0Vd0v5aST/nGSpLpzJo+32qKU43oHmts77QG3L07zZEc9kiUBrDe7TNcKfO7GEl4YZjtokHD9gO7Q5Wmzy3yjzHcfbdE9RNkG6Awc3ry2wM3FSX7wZCd7XJFlakVhBeEHEaauMpESCWRJxlAV+l7Abs+BRLjHDjyxYLspCFqaghfGtLt9EmKCKBEiq7EoBYaxxFythKooKKlXkx9FKLKM43m0+i5eEBCEQq2hUS5QtAwGjs12u0fO1BgOhyiKKGGt7bZZnq5zcW6KhBhNlbkyPyFmoGQxYxUliVCPiGOCMKFcsAjSDKzdG4IkPKzypi5eg64RpLp8SQKBH9IdOtTLBXZbHYoFC02RWZisoMgyA9fD8UOG6ef1cLNJEITcvDBJzxZZ6dp2k0a5wJ0TWXkWXhhxcabOxZlaNlw9dANaA5eh4zPwhP2GFxy13wDo2Q4fPm1yY3GSb370FMcLKOdMqkWLUm4aXVUwdDF/JsERgtEoWzpJbPYsZb6TZhpVVT1iUDgeZynVjYMKPFuq6aQYB7ZisUgURRmh40VnoH5c4yVAnSM8z2NtbY2FhYXM0wWenxHpuk6tVmN7e5uZmZkjvz9KVhAZURBG2K6/D0SeTylncXGmyjfvP8HxvGywdQREX+/1+OWfepW715d5uNminLeoFkUfxzIEWUFCWIbbXkDf9mkP+tkuN4zE0Otnry+iKvLx4DF0WNvtcfviDI+3WseWchw/xNQUbC/hw609Bp7YQYNYULe3t/jpu7e4uTjB195/cvRNkxKe7nW5PFvnTVNHkWVUVRGU8ED0zpo9h5l6AU0VrLE4iZElGDoBQ8dFU2VaA5dyzhRzT+G+WeHADVmamaRs6WkGJTFVK6IpokTohxF9x8cLQmRZxlsWtOHOwGF7ryWyoyRGlmQc1+XqwjSXZiaw3YBq0eLWpXm8IEbXBPFERqJayGXluq7t4fsRXhjg+gGe6/LKxQUhT5SW5/wwYqKaZ7fTR0JiuzNkslxAlR2KOQNJkrgwVSUhYXmmSrvvsJjKPoHIKtd2u9xammI9lVZq94dM10QG2BrY6OnCF0Yxm3sdXru6RMHSU1aeKMeNK5PvdIZoqsxkpcBX31vNpJbG47sPhf3GxZkajzb3SSQFU6dWzFHKG8RJwuuX51FkiSgRowSjfuXmzh6SLPH5W5fxfZvBYJABURzHaJqWqZ6Pi83GcXxqYVl4tqrDYYPC8b87ay+pWCwShiHNZvNcQ7yH7TRGdPbt7e2Pbcby446XAHWOyOVylEolWq0Wk5OTZzq2XC7T7/fp9/uCLprK16hqCkSeYM25QcilmRrff7zFbndAGIQZUWEERJX8q7xxfYG/ufcRlmVRLpUo5izqJYtSTjTPFyarLE3VM9bWwPHZbA/o2y4raxv8/Ju3kIAPnu4cudYwinl3dYfby1Ps9YYEYUitmKdcMMmn+nWqIqPIEldmG7QGzlgpx8dL7dLrpTyvLE5ij4ETCPZWvd5I+1Fv8NrFWXqOS9EyMXQ1WxSDMKJvexQsnUebbVoDG8fzGW18J8p5aqUcOV0hjBKktC9mpwu8psg4nlBNUBRhB788XaOcMxi4IXlTxzI0hm6IhMTA8VBkiXdXRI8uisTcklC/ELpxrd4QXddRFAVdU8gZOmbaKyrnTbxAlJluzNf5zuNderaHF0T4fkilYInMG+gO3Oz90FWNSAt5uL5DksQEsVj0PT9kYaLCXnuAJMFkWXg21UsWhqbg+SG7nSFJnIgenRvw9o0lXF+oUIyEXcdZcbudAcszE1ycqdPs20hILE9XhW18yuAbOgF5S6PZs1nZaWO7++95ds2KwutX5viH+0c3F4ossd0ZsDBRoVHOo8oyWpqdO35A3/FZ3W4LRXdV4avvrx7ohfq++C/wfH7u7g1838eyLAzDeOYCfxZhWXg+0IzUUA7Tz89DdqhUKrRaLTqdzqkddMev83BpsNFo8O///b/HMAz+4A/+4EzP95MQLwHqnDE3N8f9+/exbfvEJupxMWrAPnnyhFq9QbNn83Svy9DzCcP4AGMu8H2uL0xy/+EKiqKiaVoGRAXLZOgFTFaq/NLbryBJEpqipM6pglDwtNnD0jUmK3n+/r2VI9eSLxT462++x5feeY2FiTJr6QCnqghL70rBIm9qxHHC3ctzB5xUm31blHJcn4SEt64u0Orbxw5yNntDNtsD7lya5evvP6FctKgWLIqmgWmoqMplVEXGMjQMXWW3Z7PZHjBwPWzXyxbF6wuTzDdKByRzQFCinZStFqS7YV1VUGUhSWRoCtoITCUJQ1O5PFlEk2X2eg4rWy1+7sYUfUeARTlnkiTQH7rpDJeOKSvkLR0SMUQriBYTKIoESARRhOeH9NOyW892ma6VkIBG0eC9J/vvS99xhE+TMrbIypA3hBuuKstEcUKSkja8QIBa3/WRJIm1vS5BGDHXKGOoihByTXUCdVVlfa+Drqk8bXa5NNdAliVKlkGcwHStiKYI2nkUxyxPN4hi0UOM4oQgithMP8OVjS1iWeUzyzOsbrePgBPAD55s88bVed64Os/AEeKvujYq5YqeYqvvUC2YfLTeZK83xPMPMkOJY37lc3e4Nlvj//7g0T4pp1JBihMUQoaeT73RwHPdoxdxTJxWWBZOBzTHDd+OEyvOEoqi4LruqR10R3FcliRJEr/3e7/H7/3e7/GXf/mX/JN/8k/OfD0/zvESoM4ZsiyztLTEysoKi4uLZ9pJjabWn6yusLC4yD987wOGjossS2iangHRRmvA4lSd/+eduwwcn7yho41Rch0vZLdnUy9a2Zd/1I8Yj1LO4PbyDN97vHng8ZxpUi9adPs2y1O11KlVOeCk2hq4rO32WJqq4vlBxrg7HD94ssPNxckDg5yVvOgpFC0TK+0nvPOZZcI4YegGDByP7VQu5+nmFhdmp/nMxVme7nTwjmmMf/h0N+tHPd5qUS/lRN+iYLE38GmUhB6flBr79RyPrTTrWN3tMlEwsp9tN0DXFGZqBX765jyVvMlWx0aSEJJDScLFuUnxfqdioJoiMzJ6avYGhFHE06bwOxrFVLVAGEf0ej6qIvOdR1u8dWWOlW2xCZGAomUSR4JmvjxdA0BRBMnDDyPc1IjQSTPQzVaPSt6k2bPTzCvJHr+1OIEYlRVuwnlTo++ITUXRMJFkGVUWjLw4FuU+23Np9W0koF7O89H6DmHaswlCMagMMDNR5y++do9y3uLVS7N888OnlPPGATKEmoIdpKy8Zj/tQXk4bpDNyb2yPMvyVIXvvv8RcZIcuM91TeO7jzZ56/oCv/DGK4KBaKjoY8O+PdujM3ApWTrBGZl9zxKWhdNr942Gb88KLMeda8QS1DTt1Bvc4zykQPTK/uAP/oAvf/nLXLx4kcuXL5/r2n4c4yVAvUDk83mq1Sq7u7uZ8dl4jMgU4/+FoehlGIaB53n0+31+5u4NPni6R6OUE8rSh2ZDJCSShLR8s0/JHcXluQYXpirH0n4BfrC2zZtXFri9PI0iCw8kTR0BUUR/6NAZupRyBt/8aB3XO+qk2nNc3rq6wFSlwHZncOB35bxJ0RKN6TevzBMjsrDRDFTPEXYNfhjxyuIkD9b3jjxHqVTh/YerTNZKvHZ5NisZmbpKrZjLVLJVWcwpTZQL2J7QhAuimPbQFRYVTmrxLktsNnvsNNsokkQUBMxW68iSxOOtNrpukCQJDzfbaIpMJW/ihjE7XZfJSoEoFqrlnYGLHwR4YYSlqVybqRBHMRvNPoamYmkq/XGAqhSwXZ+OE6DIsmD2uT5vX5tlZacnrENkKZ0RkpBkYZHRGjiMv+lBFNEdCEByPJ+lySog+na6oiIlETkz7SXKwn4jSRJmGiWGrk8QRei6SpJayyuyhBcE7Kbve98W79fidJ3/72+/y9XZOuWcQRhGqLJYrIs5g1/5/GsYmuj5vX1tAT+K01klQYbouwKICqbG61fn2Wm2WdvaJUhLnJqmoeka91e3KBfyfOmdN7i/ti16UDlzn5ijivullDfp2R5PdroMnFRFJEkYDIc4Q5tffPs2BVMjDJ+v2QdkbrwnCcvC2dTPp6ens7mm8zAFR2W6cZbg9PT0qfpHJ9HawzCkXC7zn//zf/7UMfleAtQLxvT0NN///vdZXV1ldXWV27dvZzVrWZYz++p8Pk+tVkNV1ezGjuOYlZUVrl2/wds3FsWCO0axHrg+fhAyUSlyfb7BdruHHx4l/j7c2KNeXOTm4iQ73SGVvEXR1EUfJwWiIIyoFCw2W33Wm33B5kotvaMoYm93j1/7uTe5MFnh/bWj/SjPD3m61+Xa/AST1QLWmIqAmIEK2O3Z1AoWXhDyvcebmRbeeNx/use1+QnaA+cAyJq6yqvXLxH4LoZW4KdfEQ6wx4mTmrrGpZka3/zwCYOhw+dvXWS3O2S2mqdje5BaWeRMk5xlocgy1xcms+HYYs7CTZXPwyThyVaXz12boe8ExEnMbDVHGEWEUYyhKbQGwoKgYGqYmjD0M3WFle0hU5VCyhwTquGTFQGclXwutdOQWN3pcmNxgoSEh5tNGqUcYSwo7TvtIZOVPD3Hy2wwAGHLrik0uwN8PyBvGSxMlElIuDxbY+gKtqYiyzS7NkbK/Gv1HNZ2OzhegGVqBKm5oKYqo0QLIAWxmHqpQNHS8cKIcl4YH87UiwBoikLPCWhvt2n3+nz21mV6tsu37q9m5bkw7fOpmoqhKbx5Y5kwhiCGnCHm2sqp8vmIIfra5TmGbnBkxiqKE2bqJS7P1PlgbQdnrF9ZyOcJg5C//e59vvjWrTNr9j3LMv4svaTDw7dnjXFHA1VVsxmpubm551LPTwKo0ZBusVg88/X8uMdLgDpn3Lt3jz/90z9lc3MzY+ddvXqVQqHA1NTUASA6KUZS/09WV1i6sMy7j7eyss547Hb6TJRzvHpxlm98+PSACGfBNDB0Iao6US5QK+boOz5dx2PQOghENxenqBYsPlrfO/D8iqJQKpf42++8zy++dYu+I7yHSnkD6xD1PIhiyjmTR1ttIU/keAd8kyxD482r81SLOfa6Qw5HezDE9kq8eW0BxwsyooUsiSHSvu3yYKPJpdk6j7ZarO10M4biqFwUBiE5/SZvXl3gL7/xHpqm0ndDcqZOyw6QJAFEiSJzbb5BSopMqf+w3uzjBIFQcvBCNlo9VFlYdHx/ZYc7y5OCGTdRYLvrYHtiBsnSVXJGat5WL9Hs2SBJTFWLWWkulw5AlwsmsnyFJ7sdliarrO60uTnfYG2ni5aCuiwJQoala8w3yjR7dmbqJ0kSE6UC3/5ghYJloGv7Iw3bHUFjVxWZOxenWW/2mCjnIQFdFYuf7fnUS3n8IESWJWE5EsPipNBxK6bGjXESc3GmQc92qRctwlQ7bzSse+/DxwR+gOM4fGUw5Fd/+jUWJyusbrexcjk0VcPQlAyIkiThp165kN37hweswyjitUuz7HUHrO50jtwfm80eeVPn7uU5vnZ/FWKojHqWF2eyeS5FlklSNt/z4lnCssCZZ4hUVaVWq7Gzs3Nm2aLDRAdd1zPlivn5+edmcidZvX8aKebwEqDOHZcvX+Zf/st/yezsLJIksb29Ta/Xy/592rAsi8FgQK/b4daFKb754dOs0iOz/+U0VAVTV3nn1oVUJ08sJD3HY9geMHBdqoUcFyYrfH9lg+O+t/ef7vDZ64tcnq3zYKNJ3tSFyVzOPEA9vzhTx/FDUfdvHaSey5LE29cXyZsaG83ukXM4XsBHG01uLEzykbxHKW9QMAwMXdnvb6U7Y1WRebDRpO94OJ4owwRBQLfbpTuY5c7lRb5//zFhHO33LNJFsdm3mamX+JXP3hZlM0041UqSjESELEnsdm2mKjniBDZaAxbqBeIEuikZQpElBm7IXL2EoSoMHJ+VnQ6vLU9i+yGVvEklb1LOGbQGHoYmkzPExkOWhNKEH4QEvbbIAAAgAElEQVTM1lLB2ERYeTT7NrqWEhGimM12n9maALE7F6fp2h5xJGjmF6aryJKELAs2YqYAH8dYhsZX7j0mr0m8fesyl2aqJIm4bhgx80bqF0OiJGaiXKBasPD8kMlqiWa3jyRJmLrGwPFQFUWU0HY7yLJEq2fTqBT4h3cfMl29gB+GIgv2A1RLoVLI4QYx1VqVbrvN2m6HV5bnuDDbQFOUrAflBmK27Mlul0YphyJLfOPDp8fe899/vMXti9P0HI92f398oZwX/cScLkpgn7txIe1BCUuVvuPRt33Wt7YpF4u8cW0R3/dO5c12krAsnI+NpygKuVwuy35OS5Y4zhMul8tRqVSywdvj1o9nvcYoig444Z4l4jjmD//wD/nggw/QdZ0/+qM/YmlpKfv9X//1X/Mf/sN/AODmzZv8q3/1r154CPos8RKgzhmFQuHATTExMUG326Xf75/Z+KzRaLC6usrFS5d44+q8sEdQlezLaXvClqDZd7gwVeFbD9bp20d1yoaOT72YS2VmNrLHRxJC5ZxJFCdM14rM1sU1jna4m23hdrryZJ137t5E1xQ+OKbUFycJ31vZ4vXLs+x1hvQcl2oxRzVvUbD0rL+lyBJX5ht0Bi7tocugKco4tisWCFNT+NytZTrdLk82hQK3pqmoqrDe+ODxU+YnG/zy5++w1epRyplYhoo2UrSIYyHmaukkCazsdPjspYm0xCks09f3erx5cSJVTddx/CBTvDB1lQTxxV+eLIssQ5b4tbevM1vLoaXzNGEQMF3JUSuYbHeGFExB19ZUBdcTzfqNVp/FyQoLEwUhqCtJwp5dlvjM8iQF06SYExnLbK2AliqtS5IAFi+ISOKIxckaURTT7jtoiowfCE2+rhcRBCFzjUpaTlQwNDGYnCQJixOVbHDbSuWo2gObmWqRj55ui3k6WWJ9r0vX9miU8qys7yBLEo82dlmeafDnX/0emqrg+AGGoTGqzr59YxnS+3G0ueg5HkVL58F6i9bQxvUOZv3re13eur7A9fkJ7j89qrUYRBHdocvtC9PYXrCvUpKWivuOz263xdJkmc7A4d3V7QPHS6rBg9Wn5CyDG4uTZ9Lsg4PCsnA2g8NRRFGEZVnZ5vQ06uej447LdkqlEmEYsrOzw+Tk5JHnep5R4Xl7T1/5ylfwfZ8/+7M/4969e/zxH/8xf/InfwIIC/h/9+/+Hf/tv/03arUa//E//sfMl+rjipcA9UOKEavvo4/ETNJZbpiMer66yqXLl9ls9dls9bMG8XioqsKtpWm+9v7qkecxdZX2wObidI3PXl9ElqV9xl+qnrDR7GEZGhPl46nnuWKR//Otd/m1n3mDC1NVVrbb4vVJUC0I6nnRMoiihFvLU+lskPD26Qw9hm4/k7N5+/oC/aHN9x48xfd9wjAQ9GpVUObfX93m7VcuEaFimdqBbG7cMnxhosJu16bV72ckkVFZcapa5MbCBNudIaoiYXsCUOIkYbFRomyJPkwpZ6Apws/pl+5cpJY3ieOEmws1JISzbhhFwtNKyeOnJo9+ELC1tcXCwgILjRJ5XcWPYqarRX7+1YtISOliJwRWZUmAXJJmWUsTFSTIBnMBJsoWfkoiGDr7jLSnzS4LjTK1Uo4kEQaMjbJFJW+KwWlZsAhfvTCDnEDe0onimO7QxQtDwlDICiHBxm6HSzN1dppdJMDQVNq9IXu9ITlDZ2G2gSRJPN5ucefKAvOTdWF4l4JRHMdi6BlY2WpnpWI31cr7hbdfZXGqzMb7R7PoKI6593CTN6/MIcmC5HOY+COAKCBvqnx/ZYeB7R4oFQO0BzZvXp1nabJyoByoqgoTE3WarTbeTB3DMM4tLDuSCTqP+rmiKJRKpWd6Px2OZ7lqV6tVdnZ2jgWB5wHUeYd0v/Wtb/HOO+8AcOfOHd59993sd9/5zne4evUqX/7yl1lbW+M3f/M3P1ZwgpcA9UMNwzCYnp5ma2vrzJbPhmGQy+XY292lUa3xcLN5rBr04409GkWLu5dnsb3gGOWGgGY6d/LhepNW394XDB2LonU89dzUNMqTEzS7A5YmK0xVC0e8ffqux2Z7wEytgCxJfOODJweccUcW7YHn8HN3r7Ox26Hvitp/3tSoF/fZikgSn791YV8Q1vHSbM5PGXjw869fp5kuroejO3SIE5isFMX8UCK8oaI44dZiHVNTs2ygUbSI4gRVSpClmDBOMp03SRLzRiDIASMCh67rFIpFNre2mGg00DWFfk8QNQqG2ISMyi9JHBMkMUl6wpFF93goioIsK6LPhMTPfGYZSSIlhAgJJ1NXiZOEiVKez15fgCQhSWIsUwjoVgsGc/Uiez0bxw/ZaraJooggjAjCgPXdDtO1EjnTQNU0kvR5i4UclWIBJXX2jeOEMBTZoGmoYo4sjAhicP0wI3nsdPb9sEZaeX/37ff45c+9xqsXZ3hvdXtsbk4Xc2fp65soFzLiz8DxGTheNgohAa9dnuPSdJVvjUkqjcL1A76/ss3t5am0N6emupD792PfFhYthqoRnZLZNy4sq6rquUp8432fs9DPnwU0kiQxOTl5rJL6s457ER2+wWBwoBI0cl1QVZV2u83Xv/51/uf//J/kcjl+67d+izt37rC8vHyuc50nXgLUDznq9brooXS7VKvVMx1brVZZW1ujWCxxda7Bo80mtaIgQwggGmUVEqAhS3LKbPMPSAgBXJuf5MJkha0TqOfvrm7x9rUFbl2YQpbkA1/8MIoZ2B6doUsxZ3Dv0Sa24x9RPf/wscSXPv8aE0WDB+s9NHXfGTen///svWlspPl1n/u8a+17kSzuzeba+0x3z/RsGo08kiOPbPk6sAeOkShwEDvJByMQgjhfAicwZCFGYkCIYxsBBBhBgCBOEDjItS8U2/fKWmZGo9H0TPf0ymY3972KrGJtb73r/fAurGKR3c0e2SPFfT6xWayF1cX3/M85v/P8VHLJKJpucuXMGKbldCxv7qsVDWaG82yVa8ytlTpeo6KGKJaK3F7c5NRIH+/cXgz8m/xl32w8guFhmSTJHaCHZNFj8rlzPNO0MAwdRYxgmD4pXMLyuIJhWexYQlVll1nnRzweR2+1EGy3AtR0g6j6aANK21MNth80LMvCsW1k2a0Ok5HOC4uDg217jrs4mLqOaZrUmy1CioRtO+zu7pKJu5Twcq1BbzZJLBJCEkVG+nKUa01U2a2ECplEUMGJgkjTMDAaNqZtY9k2tgO1ZouBvGsH7ziu4q/ZMhBwSCdiiKIrsBBFyCZiTA7kCatuGzcZDfPymRMdC9ztJJHR3gzDPSnWS3sdHEf3d4Xr8+s8Pz3M9FAPK8WKu1Lg4bjaAcW96TjFvQbL2xXXxLLpdhfK5QqCAJ97/iyyJGNZjw+Wbd+ROu5cpT2pHfR+ethe06OS4VEk9YdZvT/J6/cjHo9Tr+8f/NrdiNPpNOfOnaOnpweAy5cvc/v27acJ6sc5BEFgZGSEu3fvBnyw49y3v7+fhYV5pqen6csk0Dywp48Qqms6mm4wmE8x1pdhubh7qCDi3uo2z8+MMDWYZ3O3Sibuss/aTeYsyyabiLJdrrs0As0VQximRUtrsbu7wxdfe56BVJS/nFvoop4rqsLsSpGz48MU8lnCqqvo8pOoDyW1HQdJFHj37mpHEvXj+rzJxYkBipU65fo+KUAQ4OTwAFgGjuPwwswIDgTOu3XNcKsg3WR9t4YoCJQbOqqXoHRdR5HjGN6FUZGl4OtQ+9eq3NFekiWRlt4pYc5kMoRVV66vmxapyGO0VDzSgH1ADm07TtDiM/0Lqnex9CvR3lQcK+4O4RVFYa9WJ5tKBhL6SrVGLO6qNj99fhwH198rEw8zmHNPxLbtMJBPeQ/vdIlaDNOikImzXa4xMdjDvaV1wPHeJ4uGZpNLJXjp1AmAgMVX11zvsAer28iKzIXxQebWSodWuItbu8QjIS5PDu3vtiky2WSUtFdFCwj0ZeL0ZRI0WjrVpk55p0q1ud/OnRrqIZ+Mcmdxs4OwnkqlKJaKvHV9js9cnAacY8nPfcDsceNgovEVuY+z1/Q46t6DJPWjZlc+R/BJE9TFixf55je/yRtvvMGHH37I1NRUcNvZs2eZnZ1lZ2eHZDLJtWvXePPNN5/oeZ40niaov4JQFIXBwUHW19cZHh4+VqtPURSy2Szr6+v0Ffq5em8luJC2x2qxQk8yxoWxAT647woiEhG1bQFSRhYFCtkEfZkE9ZYReDW5iU7DMG1On+gjHlZ46/rdfdisR7SIRCJ8++otPv/iM1w6N4Vl2aRjEU/avq/KMy2bXDLmnm6brSCJBr+TJHJlZoRCOn6otLjWbLGxU+XciQLlutYphrBs6i2Dle0y/fkU9WaLG4tbgXptaiiPg0hd0xEFiKoyiiQFp3VFcvl5XV/L+z8T8lqCfsiiiHagLSqIIj2ZJPVGE003kOVHt4QcByRJ4CDcw7Lcis52HKqVCvVmE8d2kGUpUCuKkuvVNDAwAIBpO0TCKg4O6WSaB0u3kCQJqe11+L5Y/m6SZVsokhioDn/mhRlMy8G0bHTTwrZtetJx9upNJgZ7uL+8iSxJxEIuONcBEMCyHOqazkcL6x2VpmXbbC2toSoKp0Z6eW92ucMO3kdmWbaFqkjdu21trT9FEpkZ7mF2xeUWHozZlW2i44NcnBziB/dcdWAiEiKbiHJ+rIDqVeeyonhWJ51Jx3EcDMPoWJrXdXf+F4vFjt3mO+znffq53+I/WPEcJxG2k9QHBwcfuQP1pPG5z32Ot956i1/8xV/EcRy++tWv8od/+IeMjIzw+uuv88/+2T/jH/7DfwjA5z//+Y4E9tcRTxPUX1Gk02nK5TK7u7vHhkImk0nW1tZoNhucGunl+nwnXsiXh9uOQzoa4pUzrvTcdhwaukGtoQeCgkw8wmA+yfdvPkBrmxO5RAuB6l7FpZ5Pn2BubQdFkcglY8Gyr6q4f4STA3lMy6ba1NmpN6mXDGpNzWsFweXpYeJhtcP63A/Dsrm5uMW5sT7qmk4kpHimhPtiCNuTaKdi+ztWtWYrUN3t7VV5sLbFa89Ok4mFKXny5LAiU21ZfPrUEA4wkosji0KQ1GVRpOZVKbIoUvPacqokBkif9moKfGO/7lN4IhKi0WyytV1icuDRA3HHcbBMi1q16lZGho5t2R7fz52DpJJJ4okkgnjgBCwICML+waZabxJSFZqajiRLZLNZtoudBBO/peiHadmEVPfi1dJbgaBDlQV3ZmPb5BIRVoq7xCPhIDE4OGztVhnty1D3DjWjvWn6M0nW2lrGkiiSy+e4cfcBA7kkz00NUWvoHQviLcNt/S1tVRjKJ9ncrXH3EGUfQFhVOD/Wz7t3lzDalpZ9FaplWSSjET51xrWrsR3HE1u4pJK1zSK9+TQzw32Ud3fQNC1IRLZtB0vzoVCIRCKBqqqBT9vjgmXb/28PO3j69PPD5OfHTYKhUCjYkXKB0j/8BCWKIr/5m7/Z8b3x8fHg6y984Qt84QtfeOLH/7jxNEH9FYXf6rtz5w6xWOzYDpp9fX0sLS0xOTXNM+MDKKKI4rXPHJzAvXZ1p8ZgLsEP7i1Ta7aDZvcT0RufusT58UHeuXmfcNj941QkiUzSneOYlsVwb5ahnkyHpYK77NtieW2TZ2fGiIdVPjogqgB3lvDR/AbPTw0FKKSwKpNrQxT5ie70SJ8Hs90XQ9SbWjBHujIzgiqLrB2w90gkEhSL29xZ2uT0aC9L22V6UwmiIYWqXqOQjrjCDENHEgjsH/yZmvu1ELTyZFmk0fCSlSJ1zEdEQeioBPyIhxWK5Sot0yU4+GE7HuTXe891Q/dsOGYCblwsGkVRU4ji/gXKcRwikTB1rbti8KshP2oNzX1OD1vk00l2dnaCA5Bt2yhtF0DTNIME5f4/ed5lXu41vN9Da7YwLYuZkV5EAWTJNWsMKQqlSpVIOMzNpS3OjPbiODbhkEIiEu7g5emGhWk7RCMq91ZLHQvifuxUGzwz3k9pr3FoO3Bjp0JfOsaV6RGaLaMTOuutQyxslj1V367rZdU2E221dFY2NhFti7GBPIZhkMlkHkk/Pw5Y9nEiFothmiYbGxv09/d30M+Pa1QYjUZJpVJsb2//jVvShacJqiP+/M//nG984xv8zu/8TtdtX/nKV7h69SqxWAyA3//9338kWkSSJEZGRlheXmZkZORYH3xJkujt7WVjfY3h4WFWS3sUKw1qWgvdsAK6gmEYiKdPMjPUw5985yqyIqN6PjnxeBxZllnf2WNmuJfXL59GFIU2CKe7ALlT01AkF7b6nY/mu9SDohLi21dv8sVXLwdLvn6oskguGSMVC2NYNpNDeaaHXYCppneim+pai3NjA7R0gztLR9h7LGxy4WSB0l6dalMnFQuT9YCz4ZlhFE+BNtaXZX5rj4GMSFMzkDzfI3AroKbufu23IME98ftgV0nY/74qScGJXZZcwcRhzZiQIrFRqmBY7rxnfWPdwyeJKKoSwE+TySSiJ6dOJZMI0uEnXLcFePhnwmmTpfthWW4C8j9HiXiC0k6JWrVGPBHHth0EZf/xWrqboI6aThim5SKQAK2lk0slaGgtVywjuMDWte06w705elKuYnNysId6y6DS0Njy0FMNTWe3XEYSRX7yylky8XCH8s+PvYYWmBTOrRWJR0LEfSSX1y7WdNOlsqsyd5eL1LQWWqvNgsMwWN9K8uK5CeZX1mk0Gh30c62psbhR4uRQHz09vccGyz6M2eeHe3h4+MwnlUphGAbFYjEQGTxMYv6oxyoWi8FjtT+3v4/1f2o8TVBefOUrX+G73/0up06dOvT2mzdv8vWvf/3YewCJRIJ4PE6pVAo+qI8b0WiUSqVCsVgkForyzsISRhv7TFUUVFXlzvIWr5w7yetXztNoGYE7ri+GMC3bpaGHFRY2yuzUGofuWF2aHOLciQLXDlRJiiKTjMeZXy8yNdRHOhYOZkTtFIG10h7JWJhYSDnUHwjgo4V1np8apj+bYH1n/yLWPj+zLIcL4wNI4v4MqtposVWpU67WWd/c5guvPEsspCAIrgFhSJGCBCWJIoZXKUmCECQlUdhv/UltiUuRRRq63/rzkE6e3YlbERnEQgq2PURxZzdoz6mKTCqdQZYO/zNyHKej0joY9kNudxd5Dyxr2jaKLHvyb0AgMMBUVdU1TmxrFTZbOj3RJEdlKNMyCSluZV+uNUgnYuzV6iSiYaoNDUWSWd7cYfrEIB/c36BlGpw70U9ElZk7gMtKJl2xwvduPuCVcy6zb32nSiYW8Yj2rrWKInlL3IN5KvUW5XqLWqkaLHEbpoEkOLx6YYqI7HBjcdnd55Nd6GwkHKZpwtzaDq8+e4qFjRKxSKhj3QJc1qAgiEhPoOx7VJJ63FZdLpdjfX2dcrlMOp1+Yqt3X1ln2zblcrlDHfxxlnR/HOJpgvLi4sWLfPazn+WP/uiPum6zbZvFxUV+4zd+g2KxyM///M/z8z//84/92ENDQ0Gr7zAJ6sMGuLIss7a2xuTUFM/MnGR5e49kdP9i3i4o6EnF0XSDnbrG9l6TerNFXWsFF+7TI30UsnGWtncPfZ0fLbjS84mBHAJCBxnCPd0a1LQW0ZDKnZUi1abWRREQRYEr0yNMDua7mH/gJoydaoOpwTxD+VTHDMqH5c5v7tKfTWDbNh/c724pirLCX7x3k598/iyC4CrrEmElaN+J3lwB3Farn6zaqylRFDEsC9MwEIGmplPcLpJPx7GsHsrlsqdYVIjGYvRnk5iWTT7vtdMch558nvWNLXr7ehEOyQKOp7g7KpyHEAxs2+56TMu0CKtKx5xJEATy+Tzb29tY1kjHbbVmi8FeBds5nFdnmFZQwW0Ud7l46iSGaaIqEudODiLLIrMrW/zUSxKaN6O5sbjBlalhTo/2cauN8JCMqoz0ThCR3fbq+ECOqaEeTMtzyW222CzXA4n4hfF+JBE+vPugCzqrKgrv3VnkhdMnMGyBYrVONhEjE48QD7vGkLKX6Mb6c+xUm2xXfHm7u25RLBVJJeJ85uKMW10fEyz7sNbZ4yaog/Lz43L7/PCTUF9fH6urq8iyHHRvflycdOv1OpcvX+Zb3/pWYPI6OzvLP/gH/4BvfOMbR6Ka/sYlqP/+3/87/+k//aeO7331q1/ljTfe4N133z30Po1Gg7/7d/8uv/zLv4xlWXzpS1/i7NmzzMzMPNZz+pSJ+/fvoygKq6urTE9PB4nIcVy6gj/AjcfjgX01gKZprCwvc3J8gvH+fMfFvFStBtDWoZ40A7kE944YQt9d2eLKzAjj/Tnm10tkEhHS8SiJSMgbbIuIosBALulKfWsada1KVWuhaTqmbbO5sclPv3qZgWycaw+62zi2vY9CsiybkCoTDbnLm+0+VrWWQUSRubm4Rc2bQbXHdqXGlZmRDiNFgEwiwumRHmKe/bvtOFwa73OXTm2bvlTMmzt5LT5BwDBtLNNEEKBSrVHarSBM9VPcKbO7W0EUBzEti2QqST6bwoGuajcWVjs8qmzbIR6NEg6H3VNtunvnzZV+P1kFZXsopPbQTZMYrqKwPWRZJp1O02q1ENj/Q681mkiSiGMerh4zLTvg+lUbrrzfn1n1ZZNIooRp6IiiwNmRXhBAENwZZW8qRvKUmxDbDxjVZos7ixvk0kkKmThv35in0Wp1LXHv7O7wUy9d4NLMGLcWN1AUFUFwPcSyCfczaVo208O9nBKFQN7eXnFpusGz44OEFImlrf1DlyBALptja2uT799e4IXTY4cq+w6LR4Fl4fj0c19+HgqFjj2Lhv0dKH8NxU9SkUjkSPn5j1rEYjFOnjzJrVu3ggT1O7/zO/yjf/SPHsoR/BuXoH7hF36BX/iFXzjWfSKRCF/60peCXu8LL7zAnTt3HitB/dmf/Rnf/va3mZubo1qtkkqlmJ6e5vTp02Sz2Y5EdFSEw2EikQjl3R3iyRTv3lk+lDKxsLlDPhXj7GiBG4v7yj+/zRKPhHAcGMglGepJuTMoTfcEC1UP2qozM9xHMqIyv9G5OCuJItlslm9dvcUbLz3DQC7JdqXmiiG8060qexQBQWCoJ+Wdbt1ZRa3Nx0oUBJ6fHqYvHWO31uj6XQzT4tbiJmdP9BELq27bUnEJC7v1Fkvbe8wuLNOTz3JxfBBJEtBaBuOFFJIoEgvJ7JRKCMIQG5ubNFsGonAC07JIJBJIkkQslqBHDrkEcEFCVVWXk3fIexsPKzS0/XmG7biy8GQqyfb2No1mg2ikszp+VIvPcQ646raFfcgMyq9WxUPmH5FIBAQhUD2Cq/x7KGTU7ET8tHSDRCyKIAh8eGeeK+cmOTM+HAgWmrqJ7Vho3qJ1IRtnYWOX9Z09NMPENEx0XafZbKK17vP5ly9xcXKQP3/vJqriLnErioIoCsTDKqW9BkM9afLpOJIoBu3o9oorHlXpS8f5/p3ljt/Nj+sP1nnuAPdPxDVinBw87S1t2yhqCL31eG68DwPLwvHVeL5kfHl5+dicTuhc0vXNDtfW1igUCk/s6vtJxLlz57h58yavvfYa7733HnNzc/zu7/7uQ+/zNy5BPUksLCzw5S9/mT/+4z/Gtm2uXr3Kz/3czz3WfXt6enjzzTcZHx8nEolw9+5dcrncsenD2WyWpaUlYrE4EwM5Zg9pn6ViYfYaTQaySV44NYwkSl1/9FuVOvGISm8qxtu3unl+sF9pTQzkmVtzn0cWRbLJCOlYnrAiYdk24/05JgfzAUXAXyb2KQLPjA+gyGLH6dYPHzp7eXKQ7Uqdpm4EQNt2Fp+DQ28qxvxWhdJenUbLrWJs2+Ls+DBj/TmWi3v84OYckijwhZcusFWuMZiLY8+MIYoC6WyOhO1KsJVQGMlx2YJ+1SaIQqD6U7zdq4MRCyusbLdv3DsBzieXzbG5tema88ltqrlHXDxs2wnEFN232V1Nw7pnd35YggKQRJcFWKvXiXtiHsszLDwsjAMMulpDIxmPIuByCW8+WOEnLp+hWm9iOgJ3V4rgOIFkfmKoj/HBHq7evodp7hPnE8kEoZbK29dm+fyL5/nsc2dp6oZnBy+hSCK2A03dYKvSIJ+M8GBth/XdvW4PsV2IqgqXJwd59+5y1+8Qi6js7DXozybIJFyKejuWq1Jvsnhvib5choFcAkN/PNGEJEnBPOqgsu9JZkmhUAhFUSgWi49lq9EeB1uDfrvv93//93n99df/WuniHyfOnTvH22+/DcC//bf/ln/6T//pI6u/pwnqIdG+sPYzP/MzvPnmmyiKws/+7M8yOTn5WI/x7LPPdvx7dHSUBw8eEIlEjnUKEwSBgYEBFhbmmZyawsEhrCguokiRPQ6dm4iKew0y8Qg3FjfZqzcPNQ5Mx8KcO1HosnB3vaYiVBsag7kE+WQU2aOT64ZHEWi2mFvdYqTQQzoWPlIQcXNhgyszI4z0pFnadhd0w7JLEUjFwkTDCpbtcHq0r5PFt+OS1WtaC8OwuDw9TDIic/3eNoZhEA0pfObSKWRJ5rvX77O1u0dPPs9Lp4YpVZvcXdtlpVTl4ng/Aq7gQBZFHAi4fK5gok080bbMe9hJPaLI7FT3Kz2/ggL3YpbL5SgVS/T29SJ6+0v2I2ZQj2rxHezx1b02XNfOVPB47jC9urcXCGgs2z7yOUzT6kh2W7t7TI+6dg8OsL1TJpeKM1LIU6rU2Fh354G+YvHBWpFsMs4XXrnI+7OrZJORNjt4JRDRhDy5+Jpv3dLG4wMY6c1wopBhs1I99LN6Y2GD52eGuTw5hKYbHQcYn4C+sVujNx1jbn2HjdJeR4eh0WjyYGWTn3j+HOlo6FhuvIeJJj5OWy2VSnXJzx8Vpml2tQbD4TBnzpzh3/27f8elS5eeqHX41x3nzp3j61//Ov/7f/9vNE3jp3/6px95n6cJqi2uXLnClStXgn//8i//cvD1r1CNUP0AACAASURBVPzKr/Arv/IrH/s5otEo+Xyezc3NY31IwT05pVIpitvbDBUKbJXrrJW6Cd8A58f6OVnI8P697vYZwI2FTZ6fHuLsqEskDxRWbafPnZpGOhbm6v01Gs1Wh/TaNC2+9YOP+NnXnmN6MM/dAxWdLIlkE1Fqms6JQobBfDLwDnIRSC1vsN1iMJ8irEi8dXO+Y1bh24Z/p1nnb105x/RIP/FomKF8kvXdOvfXt7BEBRGHF6YHKddb3Flx25L1lotZcqvFKI2WEdAnZN9mwdmfU+0r+qSueVhIkXFwOnajLMtGbVPvhdQQ0VjUXczO+ntJj66gjkxQjt01g9qrNb3X+3Bpei6fp1jcpq+vgGXayOoRCcpyE5Tvw3V/aY8zJ4cQBFzEkixzTWtSyKWJRcJMnhwlFQ0Ti6iBsaIiS8iiyMtnRml5LeOdqkat6Vq2L6ysMjEyxMWpIap1rQNl5ceSh0O6NDHE1bmVff5kSO3YhVJlGUkSWS3tUWu0Ao8yP2pampOFDMVyFb1t7haNRjAMnbeu3eHzV84jy4/mKPrhV1K+yEIUxSeWi8Ph8vNHxVEV20svvcTGxga//uu/zte+9rUf+VbfzMwM29vb/PZv/zb/6l/9q8d6vU8T1CcQvb29T+wdlUqlWF1dJR5PIAqweohpIMCtpU1emBlhtDdNudY8msWXjLK5W2Ozbael/fR5cXKIiUK2S3ouyxLxeILv3bjPp5+ZRpZFVFnuUP21dJNayxVbJKMh3ru3QlPbNyb091pm5+GLr17iRE+K24uuQ3EsFnPVSpF96Oz0cA+m7XBtYYtK3V1ulQSBN166QLWhc31hA8lLGlMDWSIhhfnNCtMDWe6t72B6CSqsSh0ndVEUAqqE6nkitUc8JHeBTk3bRlE6L1KJRIJSsUS9XicWi+GwL0I4LJwDsvD2sA5R8emm6bHXjqigPGGF6h1kSsUihmURwm072pbd8b436yGEU+OUSiUUVUVVVXTDJBxSGRkcDA48D1a3mD4xwLMTg2iG6WGKDJp6HU03MUybC+MF1kt7LB5o5/bk88zOL5GMRzg31s+7dxbRTbvNFTpCIuLuQqmSxAunRmkZrm3I9t6+Mk83TFKxCBdOFmhqOuUDi9wAK9tl4mGVS5NDXJ1bI9fG+1OV0WDHzfWWfHxlnyzLHZbxT0I/b58F5nI5NjY2Avn5o+Io9Z9lWXzxi1/kvffewzCMH3k1n6qqTE1NEYvF+PSnP/1Y93maoD6BEEWREydOcO/ePaLR6LH62b50dXFxgamp6YDcABAP+/JzlwYNbvtkpDfjiSH0Lvn52RMFEpHQkfiZG570fCCXRNMN13o7EvaWK8WA1JBLxlgtVqk2XdVf07P3NgwdwzR4/dJphjIxvn31Nooidznk3l0ucvZEgVw6garIgRW840BDdxdDIYxpO0FyAnhucoCWaXN1bpVypUJPbw+D2QSFTIz3729Q1wzyyQgnC2lMs5u9J0LQBgR3J6rS6LxwRcMq+gH0kWHZwZJr8H+DQDa3v5fk2M6R1Q7ecx5Hxefexz5yBuULK2zHRpbcqq/q7TWtr627w39VQVUUYtEYkXAYURTo6+sLHqPR0gmHVGRFxvQMGde3d0jGo+RSCb5/yBwI4KN5d8F6r6GxW9tPHpIkMXFiCKOl4TgOV6Zd4G97pV6ut6iXqjR1gwtjBYqVGvfXu5FZlXqTe2slTo/2Bdw/SRQCqw+fEanIEldmhtF0i5rmzl1dN94WK2trDPX38eLpMRzHeSLL+CdJUO1VkCAIgWRcUZRg+f+o8IGwB8MwDKLRKH/7b//tY72WTyp03fUS+43f+I3Hvs/TBPUJRSgUoq+vLwBLHqfVJ8syPT09rK6uMDU8wvhALpD6NnWjgwZdyCTIxMNcPcRvB+D20hYvnBphrJBhfsM9/frW2/7Cr4PDRH8Oy3G8GZTnwKtp1Bot1tc3+PzLF4mHZb5/YzaQEvvGhIqq8MG9VV46c4KLZyYxbSfYaWmnCBimRSYRZWmrwl5D61D9gZtMXjxzghO9aRa2ylyeKGA5DtfmN1FDIdSQimybTPRnuLlcoq65ldC1hU1enhlGs922TqgNFOt7L/mhSN2g2ERYodHqHK4bpkVU7f7zEQWRfC5PsVTEsscfuah7VJvDdrpnUOC1Df2k5+ASRTzMUiyk4Ng2W5tbyIpMOBSmWqtDb57+/kLX49l0KwV3yjWyybjnGLz//dmFVa6cm+LMSC83D6GAlOtNVkt7nDtRYLfW3J+NepV6TdNZ2d6lJ5PEcRyu3lo9VIn64fw6F8cHqDRaFCudOKRMLEJEcRdWn5saCkgc/mx0p96kXtRpeImuUm92Hbx68nmWVtaJR0KcG+vH8NY8HhWiKLoVpsf1O2477WBbsF1+7q+YHBaPsnr/cZCY+/F7v/d7XLx4kWeeeeax7/M0QX2Ckc/nA++oxyn12yMej1Or1Wg26iihMO/cXuy4mPux12hyxbPdOKj88yuulm4ylE8zkEsFF5R9620XrzSUT5OIqHzv5nxHm8i2XOzLN79/nZ997TnOTYyyXKqgiCKphOvX5O5ZucZ5U4M9mLZLtmjfaWl6EupnJwbJxMOHQmdt4KP5dZ4ZH6AnGUEUBX4wtx5c6HpyGa5MDnJ/fZfS3v7szZ85xcJu1acqUtC+CilSsDPl/mw3hy8WVlg/0EptGRap6OEXFUVRSCaSaFrr4TMo6+h2ndOm4vMH9YZheB5OFhvrrrhFVtxDgKqqqKEQkiRRKBT2H0cQXcK5aSErh/sJqbKM7s1k1ku7jA/3EVZlGs221y7AjftLXD41znBPChEhqNTbl60NyyYdj/BgYzdYLfBFJzu7u0TCIT57+TRjhcyhVVKt0WJpq8Lp4V4q2aa3nyd3qFE3ynVSsTCKJPDWrQUOu4Z/+GCdyxODVJst1kptgFtJYnpshJDooaMUFV0/2o3Xtu2OBXpN01xQ7TGT1GFtOlmW6e/vD8Cyh3VSHvY8Py4cvps3b/KlL32J6elp/sN/+A/Huu/TBPUJhg+UnZ2dJRaLHRtZ0tvby+LiIhOTU/RlEixvd1tZOA7MrZY4M9pHRJVRFDkwPgwqroaOZpikYmHeurGAblodScjQDe4vLPOzn77M5GCOm/PrLvtMkZEkyTWYU12Tu4nBPGMDOfeC4rH+3IqrTk3TONGbJRaSu5x8/fBbisM9aZa3y8iiSC4ZJZPw3VplBARiYYV3Z9c6ZkmXJwYoVpv84OY9ent7PfdauDzRz/Zeg1hIYaI/g2XbgRAirMgdqj1JFGkeSFARVWan2jnzcK3hj27zxGIxLNtGlh/S4nMcVKF7x8YXigBsbW0FFzdFUbwZkevcfFA+LghCV5VUa7qihL1KhUw226UAtGyHkLqfoHTDxLJtzk6ecH+g6+LvcLKQRdNN9hrdwF9BgEuTw/SkIqwWOz+PmbRraf6DO0tcOT1KUzNwBEjHIkTDncvcummRirmJrtpsUWtqHf/Xkijw/PQIM0M93F7ubk83NJ0HG7tMDOToTcdcDJIkIcv76K+VYsVbVFcCrJVPQPeX6P3KyYfz5nI5bNvuEE08ThzVFlRVNSCWHyY/f5ST7pPOnWzb5l//63/N3bt3UVWVr3zlK4yOjnb9zK/+6q/y+uuv83f+zt95oucBOHPmDO+///4T3fdpgvqEQ1VVBgYGWF9fP/Z+hCiKFAoFlhYXGDs5TrWpEVEVUrFwF5usZZokYxEWtnapNXRqTQ3dtIMkZBoGn3v+LCP5OG9fn+1gnyUTSSRJ4v7GDqeGesmlEiiya1sut0l9d6p1NMMiHQvz3Rvzh0qG7yxvdu1Y+ZGJuwvFumlyoi/DaF8aSRSDPStf9Vdttjg/VmBqMMe1eRe3c3G8j5ZhcXelRDqdDtiHl8cHabRM7qyUCMsSz08PUNcMal7Fpir7qj3/+q63WT0okoiAQOMA0kkzzCOXbP2QZMV9vFYL9cCFxLYtLNPCEQV2dnYwdAPbQx/5bVHHgf5CX8f7uLJZZGZsiEI+w0apU5BgO07XylO1rmHbNv/XT77KOx/exLA6W4eWZ8nhkyQAbtxf5uz4MN+9OX+oGebMcC/ZRIQ7y92tPseBaw/WeH56mPH+LPfXdxBFyHmooosT7m6c48DEUB7DtNlrtA5d5n5mfID+TJyVYvfBy7IdPnywxuXJIUZbJrppdic6B1q6RTIaZnGrTLmmUW1o6IaJYejs7VWxHYufvHIeq6VRqZQDmksqlUJRlCNb77rndPwosOz++3y0LXs0GiWdTrO+vs7AwEDHcz7MSdf/vDxJ/MVf/AW6rvNHf/RHfPjhh/ybf/Nv+IM/+IOOn/na175GpXK4COuvK54mqGPGw4jn/+2//Tf+63/9r8iyzD/5J/+Ez3zmM4/1mJlMhkql8kTeUZFIBFVV2auUeebkAJpu7rfm2thkhmlw5dQJEmGFqzfvBQDVfehsiGsP1njh1CjPnp5AEMQ2BZQUCBZahkkyGubB5i7VRqtD3m6aFtvb2670fKiHW4fMKizb4cHGDtODPSQiCoosd0Bt65pBqaoRUkwysTDfvvng0BbOB/dXeenUCYbzSWJhmbAi8/3ZdRzvPWm1WpwdzoEA1xfc16GZFlvlOv3ZBGVPaKG2ycplUeRgTo2H1WBfqj1ahnkkidwPx7ZRwyrFUpFkIhm06UzTRBBFxgb7iIYVopEoSkrputg4OCiKgtU2//ITyczYEKXKXsc+kd9uPRi71QaRkMorF8+xuLHF/OpWMNtwzQQ7LwOlcpVqQ+PMaIGPDniRAdxd3uLy9DAXTvZz7UFnJRwcMgyTgVyK/myyY05Urreo1JusrG9wfuokvekYtxc3OEyq8NH8Os9Nj3BquJfby1uB5Xz7/BLgRF8Gw7Ko1LWORNfU3er/wsQQhXSc967fcfFOnh9XNBql0Wjw/TuLvH7pFKlU8rFEE/D4YFk/Dttlao9kMomu62xvbwcoIP9+RyUoQRCeeEn3/fff51Of+hQAzzzzDDdu3Oi4/Rvf+AaCIPDqq68+0eP/sOJpgjpGPIx4vr29zX/+z/+Z//E//getVotf+qVf4uWXX36sHrEgCAwPD3Pnzh3i8fixy/Z8Ps/i4iKRaJStSoMbD9Y67DjAlYW/e+M+r18+xanxEbYrTUKKSDYRIxUPe5gi9+MwOdhDy7DYa7TYLNeCROdfDC9ODpGLR1g50FKUZYlUKsV3PrzD554/y2AugSAILh3CxyB5rUXNMElEw9xf9xKd1tnCEYDLU8OcGS1wY6H7IgmwVtrjZF8K24H372907IE9f3qMVDzKWzcXENr2le6s7tCTigUXRFUWgyVdVZa6BvexsNphnueHppsdajoH92LlK70M3aA3HSUSyiNJEnvVPTLpTIBZQhDcC6WsEI4cfuE6DJXU1HQkUaTa0Dh1coTrs/PBba6Kr/txdipVBntzvHdngfMnB+nLprk+u0hd0zAtuytBAdyeX+XK2QmiYbUD8eT+rjC/XuLsiX6uTA/jQNchY6emARqD2QTv3V3uqkARFd7+4BY/+dKzHS65fvg2K4Zpkk9F+VTyBGKb5Xz7/DKfjDHam+ba3BLVWrPDkFNRVH5w+wGvXTzF33rpWT64v4YIZBJRMoko8YiKKrkWLqIcQm+1jqXsa5efPyweBxR7mPz8qDnTx9nFAqjVah00G0mSgtc4OzvLn/zJn/Dv//2/5/d+7/ee+Dl+GPE0QR0jHkY8v379Os8++6w7rFbVwKzw/Pnzj/XYsiy7vk+rq4/0jvJ3ONqHt7Ztc292lpmZUyyGFSpNm0gy7LbqZIlswjUnNEyLmZE+TiEE/jv1A5iimaE8kihye2nz0Of350S+ZUa7J1QspAZtxfGBPC3dotLU2DgwqwBXENGbinbNKsC9CF5f2ODK1BAjvSkEBFKxMGHVXRD1T+WNlokiS7TalHfDuSR96Tjv3VtjY3OLvkIheD8vnuzDwaE/HWNhs4wsiQGpW5XFYJnXj3hYptlWwTjOvmW74zhUq3vU6nUcx0Hx2qKKJ+MOR6IoikxfX4Hy7i66YRBpo9nbtsNDVOieErLzBxzHQTdMFjdKnDrRT08mxfau24ZxqeXdGapUqXJyqI9Gy+C7H80xMZDj+bOTzK1sYJpWcDBpj6bWYr1Y5vxYgY3dKslomLCiBNW0r8yLhRU2d+us7+x1kPP9kESBZ8YH+N6txY4qyV+e/fDuPK8+M80LMyNYto0qy8jyvlCn0vAdfVNcu79GsVL3DgF6QEF/AIQvneGVcxP8f1dng0OAIEAy6trC27ZNPOK5T3egkNz51tLaBoWePOdPHk/Z9yiwrB+PI01vl5/Lskw8Hsc0zUMdED6uzUY8Hqdeb0d32UEC/Z//83+yubnJ3//7fz+Qwg8ODn4i1dTTBHVIPAnxvFardRgYxmIxarXasZ43lUpRqVTY2dkhn3ctxQ8molarFexU+P3ydDpNX18flUqFUqnIi+fGqTWNYCdEEvdbLJvlOsmouy/y/TuH77TcXHSXfA+SxPd5fG6imxjIMzGQ7/CEcpcrWyyurPHihRnCinyoOSF4iW5mOHgeVZZcHp83QwspMghwos8dypfrGtuVJtWm1rFQ/NzUMKeGe7ixuEU+EWGskOKjhW00wyKVTgdb+xfHC6iKzPfurnJlcpD+TBxZFN25DATVnR+2bRMLKSxvliiVdgL5vCRJnv+SQyadIhaPH7rv1K7ASqfTbG5tEgqphMMudPgwIGx7uBVU90WtoekkomEerG1zanyYnQ+qWJaNc8TuVKPZwnEgHY9QrjW5s7TJwtoWr1w8jSy6woETA72EQy4hIqwqqIoc0OKHcmm2K3VKe03qmt6hzBvMpTjZn2V+o3jozPHeyjbxiUGemRhkrbR3KCGi0XLxVeWa4brxNlu0PB8uvwvQaAxy9kSB/+etD7AcAUVVSHk7dIIAK6U9etJxPnd5hpZpBdW61W4Lv9fgZF+GudUiq23KPgBJCXF7boF4JMRYIYvxEGVfezwKLOvH46r+RFFkYGCAlZWVh1p0fNwEdfHiRb75zW/yxhtv8OGHHzI1NRXc9uu//uvB17/7u79LPp//xFp9TxPUIfEkxPODJ5J6vf5Ix932aDQazM3NcffuXd59912Wl5eJRCL8i3/xL4JElEwmCXlS4sMinU6zsrJCJpMhFlaYW991jeBaesccRxIFXjg1yom+DAubh4BcLZvV0h5jhSz5ZMwFfB6S6OIRlXhI4Z1DWHyhSJRvvX+DL37qMicLGR5s7D+PJIrkvERnmjajfVlO9GXbEt0+BqnWbHFyIE8qqjJ7xDLxB3OrvHh6lJOFDIPZOLNru+x6SJ1oNIqmaZwf7SGkyLw/t4Zp2cxv7TLWl8EwbQzTQm+1cJwwhmmytbnptm0kieiZEYqVmquyVNOdVu+2QzQSxqx1Uw3AFSDsmwsK5PM9bG1u0turIHkGdA9LULbjIEvdt9eaGvFoiGv3tujPpZkZG+Lm3JInkjj88crVOv25FOVak3A4zN7eHv/3t37A5196hlg4DBmRlmFR1Qw2yw1XOafpZGIRzp8ssFmuUjkEU7RaqpCMhbk4OcT3bi8hAtlk1CNEhAKyiCQKxMJ5dmvNoFqvai2aWouNzU2mTgxzaWqEq8UiW7t7iJLo+XGpxONxNip18tUmP/niBR6slzzmnyuI8KG9Td1wyfTAraVtak2tiwDSbBmcGe2l2myx19hPQqqqkk6nuTm3QH82SVhVfyhg2fZ43HmRTyxf99iHhyWoj0uO+NznPsdbb73FL/7iL+I4Dl/96lc72KM/KvE0Qf2Q4vz583zta18L5Kn379/vOJU8Kn7rt34LQRCYnJzkp37qpwiFQly4cOHYQNn+/n73uaensW03mRwMy3a4ubDJ+ZMFGi2daEgNlnL99plh2rQMi1hE5d7qDtWmRvNAohMFgSszI0wO5Ll3QJGnqiohJcTcyiYzowUysQjygURX03Q2yjWiIYV0LMx3jqCrzy5v8fzMMNNDPR2Ll6oskU/FyMTCGJbFYDbORrnOxm5n5foTl2YIKTJv31rAslxzyFu7ZUbyKVRFpLy3R7VaRS1ksG2HXD4f2D+IooAtSITD3f8P7cDYw8Jn3fkhSRLZbJZiqUhfb59LmjjSkB2cI0gT9YZGJuHSBz68t8SLZ8fJphJU640jyeWlcpWR/nzw70QiQbFY5P997yY/8dxZWobFjcXulu5uvcn8xi7nThT43u2ljjlfKhomk4igyiKKJPGps2PBwnVdc9tzNY8sIgEXJwdZ2SyxsF7sYC2qisLdB0tkEjFeu3yGd24tYTm2axOT9Nx4/c+mKDAz3MtuTWOn2nRVnR49H1zqx+WJQSKqRLnWPUsq7dVZ3Cxzfqyf2dVtktF91JISsCINTNtBkmWsx2T2PUw08TgW8QfDl5+vrq4Ggoj2+LhLuqIo8pu/+Zsd3xsfH+/6uV/7tV974uf4YcTTBPUxo/3U8ff+3t/jl37pl3Achy9/+cvHOuH81m/9Vse/V1ZWKBaLHRiaxwlZll2r6bU1ZoYHqdQ1dNMiFlbJJiKBnYXqeTbNDPe6p1lP+ec7nvoD9yvTI6RjITZ397qey3YcPlrY4OLEADWtRUiWu3h/hmnR1E2ikRD31kpUG90VnQA8N93t0uqH4zgsb5eZGMiTiKjIkpvofPBstdlipbhHJhYml4gwB4FV+5XpYUKKzDfeuUa13ghUj2pI5f76DjPDPYTDUXJ5kUg4hA3BoSAeVrtO4B2/v+2gPGTwbZrdi7ihcJiIHmG3vEt/T/aRFdRhB5SGpgUcQN0wWdoscWZ8hHc/untkuivtVZkc6Q/+LQgCuVyOzc1Nrt5Z4OULk2QTka59L/e+dQZzSV44NULLMLtI4u5nZ4eThQzLWxVmV7Y7dugMw3Avso7FM5MjVOpNdCvmmfC5QpRkRCGiuJL+l86MBu7Hdc8mZmO37lVEFpenhmlo+qHL3A1N59byNqdHeryVBJ1EJEQusc+iVL3P5sxwb2A7Xy9VvdaxQalUIhaN8PqlU0iS9FjMPjgcLAvH94/yw3c8OEp+/uOwpPtx42mCOmY8jHj+5ptv8uabb/5QnmdgYIC7d+8G4NHjRDKZZG1tjUa9wfMzw8Ep3r+Y+Bikhtbi4uQQzZbBvdXu9pnjEHg2be3W2K03iYYUcknXbj7qJzoEJgfzwcXE5/25dhkmW5tb/PSnn6MnGWVjpzvR+YKI56eGGOlJIQgCyViYSFuicy9WOpGQytxaiXLdregsywouhLqu8/kXzzNeSPH29Xv8xKVTxKJh3r2zRDqbIxSOUm/USSaTSJ6hIkA0pLBb11AlCd3YT0ixsBIssB4Wtu2gPOTC43LzuiugZMI1OWzprSMrHnBFD9Ih9683Wh1LwvNrRQqZFOPDA0cmPE3TsWybbCLGTtVtRYuiSD6fZ2l1jb5cmjMjfdzf2CEdCwfeTe0uyJLoJrZbi1vu+oJhdtDn17aKvHphivmVdfY0DVVRiCQTyLJrUtiyHGqazisXJmloesBbBPezWalp3F5aZ3ywl2bLOHKZ+9qDdS5ODFBtamyV99vqYUUOZpiW7XDh5CCSKHS4/W5XmlQ1jaZm8OzEAKJAhzGnILhqus2tTb53a56Xz508FrPvIFgWHk/Bd1j4i7jhcLhLfv7jhjl60niaoH5Ew7eJf/DgAaOjo8c+gfX19bG4uMjU9AyLxUoXZdqPj7wEtFGOsNt2em4XLJiWzZmxviDRBb5Nu7XA9uD8WD+WZXfNiSRJIp3N8O2rt/n8i+cpZOJs7NYIqzL5hO8LpQZzhBOFLM2WSaWhUdpzWzh1zV3eNHSDyzMjFNJRPrh9D7ttp0VVFBKJBB/eX+fF06P89MsXEEWR9+fWXNwPEI1FaWpNBNvkxTMnaegGS1tlRntSrO5UUWSRWltLNBZWu7BH7WHZ3cDY9jjY4gtCEMjlczQazSNnRuAbGnbf7ifNSEgNFIYfzi1z5fTJh1Zku9U6/bkklm2RTkRJRHxzyOmgIp3oz1GqNthq2ydqGa5qMSRLvHJ+AkvXWFpeC2TciqIQjcawBHeZ+5VnZri7ukUycqB95qlGdcMirCjcXt72FsbdisNxYGdnh42dPV57dorR3syhn9tGq8Xmbp1Tw72M5HUXPiyJCF57rtrUWdoqk45HiIUVvnf7cL+ya/fXeP6QFrUiiZyfGiMkux0ARVEx9NYTK/uexOAQ9qXk2WyWjY0Ndnd3yWQywMMXf/9PiqcJ6kc4otEouVyOra0tCoXCsfrYPpNteWmR0RNjbFdq3bsogK6bFCsNzo32Bco/37fJV+atFPfIp2LgOEdCZ28sbnZIz/2QJZGx/jxhRcQwTSYGepga6gFvqF1r6oEEvdbUmBrqJRKSuHp3IaiK3NOoezF879Y8n718mhfOz7CwuUtElcmnYqSi+4lOFAWiIYWr9ze6vJ3OT5xgvD/DcrHC/KYrbx/qSdGbiqJ40nU/4mGFnb1OYGl7mI9KUGa3p5MfoigRCoUBx1XfHcLke5iflNYyyCajrG67CarZ0lnd3mWkkOPc5CiS6JLmJX/HRxQDh+JcKk6jZVDXdDbKdVf0UtzBNEw+d+UstXqTj+4vo+tG4JskyzKqqnD9wRrPzpzAFhXqLT2QcXfMMEWBmaHu9pnPW/QxRb2paFDNgVu9ZDIZtra3uDq7wuXpYSzbQpElL5nue5bphkW9ZRAJq8yuFKk0NLQDNimrxQqXp4Y4P9Z/aDVmWDbzGztMDuZJx122o+pbxRjuwvvCeoloJMxALnksZZ8PlrUs64l3lvzK6yD93Jed/7g46X6ceJqgfsSjr6+P2dnZLhn740Q0GqVWq7FXKXP2RIG5tWKnXUabU65hOYRDMvdWS1S1FtqBZLaxs8eVmREGcskO+KYf5fl32QAAIABJREFUpmmyvlNlciBPIZPo9oXSdBY2dsinE8TDKu/cXupYJvaH5uubm3zx1cucHilwd2Ur2GmRJU/5F49gWhZDPSlGet1lRr+iWynuBU68p0Z6mR7K8YN7awFO7uxIL5l4mOvzG9y+v0BfXx+iKLKxW2W0J4XkXZiC90+VuX+EQg/AMO1HzKDMh15ERFFEEAV2d3fIHkIQsZ2j3XDrmkYyGmGV/R2yeyub9GSSpOIxNss1TNvAtCxMy8Y0bQzLYmqoB92w+GBuBT14743gxP+dD+7w2qVTFCs1yvWWh/txqe/5ZJRUNIxlOTw7OYAkiK6M27dy8WaYTc3g4sQg4HS0z/ywbIcP59d5bmKQSkNjfadKRJXJpWKko2EiM8NBRXSyP0ejZVCuaYFtRkNrBTPMCycHGOlN895s98qE7Th8eN/FLk0P9tDQDdIxH3C7D6CtNlvEwyrL23tslqs0NT34zDSbTSp7e3z60lnyyQim8XhuvO3y80dRJI6K9tZgu/xc8Ja8nyaop/GJhyiKjI2Nce/ePSKRyLFbBT09PSwsLDA1NcW5E/1UGpoHb61SbbYCZZ4iS7wwM4Iii13JCVx4553lbWaGe9BNk0QkRCISJhxyjeb85ceWJ8iY9RJduy9UU9PQWxo/95krDGYiXLu3HbSIfINCQYCl7TLjAz3k0wm3fSOLHcq/zUqdkCyTT0V55+bCoZicmwubvHhqlPH+LEvbZS6O92PbDu/NrroUi0Qi2De7v77LQDaJJAo0vQpKEgUkSTxUWt3+nsRDR/9/+K8rn04gICCILppGwD39RiMhRMFFSB3c7IeHV1C1hkY2Ge/6/oezCzx/ZpyNHddp2XFstxL150SbW3z+xQtkIgoLlUog41YUBcdx2N3ZYbtS57mZUWpNPVgxaK94F7fL5JMxFEngvdmV7hfHPo+v3cYFCOC/6XgEw7IYH8gxOeiqC5stk6rmWrmU9+osrq3z0oXTZBPhLm6jHzcW1l2BzUgvt5a2UGSRnO/IG1YJyTKiKFDIJTBMi1K1yU7RfW/aAbSjfRmG8ymWt3c7+LiRSATDMHn72l0++/xZIurjK/t86rmmaYcu2z4qDiY2X37+5S9/mV/91V899uP9OIbgPE5j9Wl84rG1tUWlUulS8zxOtFottra2GJ+Y4NqD9Y79j/boScWZGe4JXE9jnh1HKhYi4i1vypJLW6hrOnvNlteac514DdPEtExeuzDFylaJ927OdflCmYZJOh7h1WenmV3ZJqTIJKPhwLbBP9XqpkVEkZldKwWLuQc/qRcnBrFtmw8fdLdvRKA/m2RiMIftwPZeg7sr2x2PUSwWCYfDxONxTg3lKWQTfOfWCqZtk4qEODua562bC0e+r8M9KXpTMd67ef/Q2/t7MkyNFLAs210AdlwkEhC8jpAqYxgWH9yapVxvdgy+z4yPIAA373dXB325NONDBd6+Mec9noPpVUNnJkbpSSf4X9/+AYIgugR71T0IKIpKbybB2RN93FstEg2pnoy7s+K1HQfVW7KuejzH9pBEgednRtjx3tfDYqQnzVghS01zRR3t7bOaplNttAgrCj2pKO/cXuqgygPU6nW0ZpO/9eIz2LbNB/fXgttEIO3RUTLxKBFVBkHoqNirDVfFV9NaZOIRpgfz/ODeyqGtboAzowXXUubOkodDipBJREmEQyiySEhV3I6D17prj/aFep+Ibtu2956781FVVY8Fg97Y2CCdTndVX9/+9rf5j//xP/Jf/st/6TrU/J8WTxPUj0k4jsPc3BzxeJxUKnXs++/s7KCqKql0lnfvLnVs/Yfa1E+5ZBQc1wYdz8222tQ9MYROs6VzaXKIzd09rs8tBwo6d7HVXa7sy2V48exJrs6tUmvqhBXZXd704LOKZw/v4Kqr9hp+otM7mHzPTgziODYf3j9czaXKEs/PDLNarGBaNulYmEhIbZO427QM0x2U31np8suybZtSaZtXLpyiN+PSIN5/sElN0xnIxBnKJfj+3cMH7AC96RhjfVneuT7bdVs2Fef8xAimbfNgbZv14uFU6JfOjVPXWiSjEZqtFvcW19j15jKnxoZQZJmP7u3vh/ky5mhI5YVnZvjjv3gb3TDAcZC9i2EkHOazL5xnYX2HlVKVtMe1S0Q7Zda247DX0NlraJ4RZYumplOrN9C0Bj/10rM0WsaRLER/52hhawccF0UVCSkdthYtwyQaUphf36VUa3S0z/w4P9ZPWJX4/t3uamxnd5e+bIoXz47TMiwPKdWp7NxrtDAsi7G+DNfnNygf0ZYdH8hTSMd4585iB6U9HlaDz38qFsHB3T8zTDt4X6qNFivrm4TDYV4+N85epUy1WqXVamEYBqIoBoo7f7HenzvZto1pmoFY4nGT1MrKCoVCoatrsru7y1/+5V/y7rvvfuKsvL/qeJqgfsihaRr//J//c3eXIhbjt3/7t8lmsx0/84//8T+mXC6jKAqhUIivf/3rj/XYuq4zOzvL8PDwsRU8juOwvLzMyMgoJgKO4xBSFHcZ1VM/uW0PnaF8ktJenTvLRQzTm0948wrTNCnkM7x26RRvXZ+j1jJQFZfE7aOQMvEouWQUKWhp7aurfLuMheVVPvPcuYcmIN+6e2Fjh5XiXkd7KB45YCdiWJTrGlU/2WlawNV7ZnwAURC52nYCDysyU4M50vEwlZrG4naZoVwSSZa5trDFZH+GiCIdKXUGF2h6drSP73xwp+P78WiYS6dO8mCjRDoWxrYdbs2vHfoY06MFworMtfurjBUyDPfmqGsas4vrFHJpVEXmnQ9uentdeqBcDIfD/NznXuHP3rmGJMtIskQspBKNhImFQ/RmEoRUV95tWTb1lhFUu35r98JJ9wDQXpn4sbtbJh6N8BOXZljY3GF5u4Iii+R95qLXPpPb3/+aRrXZ8nBI+weNmZFeMrEw7xyhppNEgeemhqk1W5SqjQ7UlU/Rb7QMYmGFUqXBcnGvCy4MMNSTZqwvzbt3ljosU/xQZYlnJwZd/qJuuHNSD2/V0I3gszNWyLBdrnFrcTPY5/L/BkzTYLi/l09dmKZScf+GfSHDw8K27WAf7HH/dhcXFxkZGel67O3tbRKJBFtbW5w5c+axHuvHNZ4mqB9y/OEf/iG1Wo1f+7Vf40//9E/54IMP+Jf/8l92/Mwbb7zBn/7pnz7RkLNUKrG9vX1s7yhwl1dXV1eZnp6hXHeH0+7FygisIAxDJ52I8qkLU/zZO9epaq0AOeP/MUoCnBotkE2EqTb0zvaQ4cJnqw2dXDKK49hcneu+AGpaC6PV5I2Xn2V+vcRKm/Biv30TJZ+KBjDTjvaN317UWoz0ZMgnI0deAF2r+FFWSzVKe3UmB3LEIyo71SbzGztsbO+g6zp9PT28dGaED+b/f/bePEiO+7zv/nTPTM99731jb4DAAliAICmRhCgrIUXKViVUFIMV0gmphHIKqYokW1Tk+IrtiJItl2NTTiQxURRVYpEy40Sx/JqyQ1qQKBIBQIEHgAUWx97H7Ozs3Ef3TPf7R0/3zuzMgsACIHjMtwpVrB3uTO/sbD+/53m+R4TBtiCJdJaLS7ViUAMOm5UDo9383fHT61+TbNy6c4DltTSTC6s0+90Mdzbx0uvn6z5HU8DLSHcLL746gSIrpDNpbts5TE9HM6qqUZBlphYi5VgS/fQtlvdjHU0hcrJcdv+wUCqpFMt7wGxBweWQsFpEjp2t77los4gcGO1hcTVZ9XOK6L59Dit0tYSRJBtC+f3PV4zPDOZld0tQ70w2GMIaMEIMlWKR1y4u1ozP7BWfn5KqspbOVz1/TlZYXlpm18gAO3pbOXGZMd32nlYCbjtn51YIelz4nNXPn5eL5e6rpBOCcgXycjVZx+d28uF9Ozh2+gILq0lTxmCzSShFhdhqlLv37aIt6KFQuDJmH+hFSpZlBEG4ol3y9PR0TYgg6KO/1tZWfD7fFb/2uxUNksR1xokTJ/jUpz4FwN13382f/umfVj0ejUZJJpN8+tOfJplM8i/+xb+44twogFAoRDweJx6P13RmbwWr1YrP52Nubpb2jg5empknk8uZeyJjT1EowexKgg8f2MmbU0uEPK46DhEqqgpOu42LSzFzPFR52llYTejMv5CPhQ0CXYfDTj6f5/xchKGuFsI+t3kjMZ4/U2aGOe02/C47P3lzujbgFTi/sELQ080tva2c2uBEoY+3XMhKie6wl55mH4uxNKdmlinI+sjP4/EQXY0STyVZTWYZaA3gsluZWt6cwQd6aGG1lZHI+PZtJDIFJhd09tpKIsMtPS1IVguFYpFiUSeMGMSFaDTKzm0d5LNZEES8Xi8vvz7B+YUVbt85hMtuZ1tnO6qmoaGhqhqqpjP8UrkCbruNN6aWiWdqr9Wgcw93NnFuvpZkoJRULi3qNGu/x47NYq2yusrkZRZWE7gcDloCbn5yappSHWeNCwtRvE47e4c6OTFZLUMwxmfFUgm/28FdO/sQK8ZniVyBdEy3Q3LarOzsa2UuskaiYk9qEUWampt44+wFAh4newc6zDGd8fy+CocUq0VkZ18biUxh/fnNPamCzSJy99ggQklhemauRs8llDVat94ywJmZiBkCur4nHUEplsgrukaqqFyZZ9+VGsvC5e2R3i8uEtAoUNeEeq7n4XDYpIO73W5SqVTV44qi8Oijj/LII4+QSCQ4dOgQY2NjVxxUaMTEnz17Fo/Hs+kH9XIu6Iqi4PX6uGNsmNcvLSGKgk7z9bnwu51lhwh9vLJ3oINUXikbuOZI5/NkylZIdsnKbcPdUKYab0Ql8y+TL+B12WuyoUqailxS8bkdnF+M6Q4UuUKVq7ggwIGRHraXmVoboWlwbn6V3dva2DvQgdUimrENlflEujO3j5nlOIWKfZQgCIRCIZaXlnnz4iIH9wwgCgKJOrY/ta+t+/GVSirjI9tQSipvTC1VRbfnCwo2C0zNLmG1WrDZ9EgWp0uP48gUCuwaHWC6TMmWJIlIJMLR0xY+uGuQtUyOyToFBvTMrJ6WAPFLtddaUjVeu7jI/uFO0rkCCILpEmGzrWdz5WQFr9PBpeU1Eul81ftfKMjEYjH+/gf2sm+gg/+3CWvv7FyE/UNdHBjupqSp1eOzsotDLJ2jryXA6ellVhK1+rJcXmZqOc6ube01vn9up522oT5KRT2G/QPb+xBFAU2DnKzvMVfL3nwFpcj+4S6S6Swnz89U56KVAzpPnJth/0gPqmhlLZ3DatHHl5XsPwGB7T0t5OQiyUyB1dS6jCEeT6IoMj936y7cdqupF3srGHZIiqJc1lj2cuLerYp03yrm/b/+1//KD37wAwAOHjzI4cOHr/o1rjcaBeoaUM/1/PDhw6areSaTqWnDm5qa+MVf/EXTM2/79u1cunTpqpJ0bTYbXV1dLC4u0tTUxMLCAi0tLSaDSA9rEzd1QS+VSszMzDA8MsKdO/uq7GwMmm86J1NUS4wPdDCzvEa0jmC1IBc5Ox9luKuZ1VSWYknV9UpeFwGv0wxBFATYPdBBTtadyiuFubm8TGx1lV/40K34nRKLq7VkAk2D1y8tcutwF60BDxpajZs1COUQRDszK3HiKf1GW9zADLNbLewdbOeVDVEjFtFCX3cHIbddt7URxbrjqo1QNQ1B07hloBOLReQHP34VpWxzY5NsSJJEKl+gu62FTKG+p1s0nqHJ7zYLlNVqJRgMEo1GmZj2MjbYyaXFWM3PAnrqbGWXajrFe5x47BJ2Sb+RDXY2ISslEtkCS/H1998QMu/obaUz5GM2Up3NZbdLeL0ejpw4zUc/uJvt3S1E4mmC3mq3ckPY7bDrN/xLS2ukcushlwaKRZXR7haSmVkKdW7qc5E1mn1ubhvtIZOvHh/n5SLJbJ7z8yv0tYWJZ3K8fnGpQsel74vUkko2k+aefduJpTKsJDKm3RLoqb96GGKJnX2tQDX7z0yjzuUZ7mrG45A4O1d9MDJkCi+9cY6f27fjqjz7riSN93JJupq2ufzgcrhczPvs7Czf//73+d73vocgCDz00EN85CMfYXR09Kpf53qiUaCuM8bHx/nRj37E2NgYR44cYd++fVWP//SnP+W///f/zje+8Q0ymQyTk5P09/df8fO//PLLHD9+nHPnznHhwgUEQWBgYIDPfe5zuFwugsHgWy5tLRYLLS0tzM/N0dPTy2uXFjdlPp1f0A1VXz6TrVpKG3sEr1MCNG4f7SmfCNf/0I1YhWxBZk9/B/F0bSdgs1lxez389PVJ7tk3SiSRJpbKIQJ+r5NQhbBY02CkuxmlLK6MpXLlWIh1GvSO3lZa/B6mlupbO52bW+HASDej3c2spXI0+V0m4UIQIJHJc2kpxra2MG0hn+kdqGnUFRaXtvewY6ALr9vJj352nmBTuGZ0s5rKsa1183FsLJmhqzlQ9TUjtn5qfoHe9hC39LbyWgVho3JPJytFBjpC9HeEqvRisUyeTDRJKlegrzVIwOPYNIRyYibCrSPVY1KvU9ITl7e1IZVJMC0BD01+N8lsYd2tvMIloiXgZbSrifPz0ZriBPrY1+eyMz7UwRuXlqrGcyY7r6iCoHsknl+MmQbGBmEnkUhwcdbD3799N36HyNRaWmcvulz4JckUN08tx9k90EUik0OyWU2ZhMH+iySyOCQrAZeDl05dok6cFaenl9k/3FUTby8I0NHWgkNUyeYLBDy6zulqjGVVVa0xljWwWYEycqW2sr++XMx7W1sbTz/9tPnZLRaL1xTncb3QKFDXGYcOHeKJJ57g0KFD2Gw2vvrVrwLwla98hfvuu4+DBw/yk5/8hE9+8pOIoshnP/vZq9olRaNRRkdH+YVf+AXa29uZnJykra0Np9N5VddpjB+TyQSD7WFOTM7V3e8srCZoD3m5dbibbEGuieTI5GXmV1O0h7xEE2nOzq7UfR7D9TwST9eIX9vCQRxWvbDd0tuKqlF1I6kUFve3hXFKFt68VJ/6PDEb4bYNexe3QyJc9v1zSDpzsSXgpsnnYjWVYyaSIJ7JkSsoqKrGysoKa4k0+0b7uDi7QCKpx3dYrRYzMdntdhPwuREEgYDXzbFzc1jt9cetkbU0o10t5s+0EYl0FlEUcDukqngUv99PJBJhenGFPUO97BnoMDuWyvcnmsrhlKz4XXaOnLpYoxcDfQR363A3u/raeGMDbVyyWmjyuckVZMJeFx+8pReraNlgspplfjlCUzBoupLUi3KJxFP43Hb2DnaaKbo14tlyoRgf6tSfPyuXx2flrq5YxCLAnWMDaEWZi5dmqt5/v9/PWiLJaxcW2DvSh1WyY7NaCHpcNexOuVjC73ZyaXmtLGeoZv8J6HKGPQOddW28VE0rd+/d7B/q1Efb5d8BCOQKCmupDPHsGr0tQVRVvSrPvs0i4zezR9qq8SxcPubdZrMRCoXQNI2vfOUr7Nixg23btm3pda4nGiy+dzlSqRQzMzP09vZedduvqirT09MMDg4xv5YmspYy9SCusp7ISCUVBZ3qOx9NkcrnzUgOA363k939bbw6OV9luFqJgfYw7SEvsVQWV9ktu3JPsZZME/C6sVpETkzO1U1otYh6BtXyWooLi9UMOyN6viXgwe9yUFT1kaOp58qus/98bjt9rQH+7uQkuVyhajwkWkQUWeG+D+7FZrPx6uQ8FlHA63IQ8DjL3nN6oq6mQUFROHauvkehgQ9s72FyLsLKWqru43uGulGKJRKZHH6PE7fDbr7/qqaWbZUsXFiMmQa6G2+0+4e7KSjFTanxTruNW4e7SGV0F3WHZDV9F3NysexQXqIz7OWNi4tm6KOBYrFEJBLhzvFbaA95a1h7AnpXHfK66Aj79Ej7iq46VcH+KygKewc6mI2scerSPLK8/v4bBsAdzWEObO/ltYuL5qHGX45U8Tjt2K0WHHYJAZ3wkcoXKmQG61317v527FbLpvszq0XkwEg3q8ksi7Fk+fdb7ZIiKyVsVpFEpsB8NFGVQSUrCtGVKHt3DDHc2YR8hZ59sM7sA6r2SisrK7hcrpokg3Q6TS6Xu6qpi4EvfelL7N69m/vvvx/QSVxHjhwxHy8UCnzxi1/E7Xbzm7/5m1vyD7zeaBSo9wBmZ2cplUpVdvxXilwux+rqKgMDgwiCsC7Mza3TfIslPabhlt4Wjp2dJa/UXwj3l4WQRydm1/cgDgm7zWZ6q5XKM/SZSLxmD1IoyOSyGT52515mV+JMb9iHGDCK4Uo8jUOyVfn+5WXd4FbVNJp8Lo6dnSVb0PUrlbEcpVKJn7ttDKdk5UcnJ02nC4soIqJHbXgdFga62ikoRZySjZKqkpeLrKVzLK2lyORlROADt/RxYXGNhVh9MS7A7m3t5Aoy52aWdGd1px2v24HX6cDnduBx6OOUvFJcp9CX359UJkciscb9d+6nWCxVjfoqIVmtum5sOUYik681cS3bUVktIiuJbHkEuz6eM7CtLURH2MfLZ6bYuPbK5fMk4nEeuGs/VotINl+oEkdXimfbQ17W0jlOTy0j1xmPtjUH+dD4do6dmSKWzpl6Olj3/uts8mO3Wk1jXkPTlcoWiKezLEZW2TOyzXSAqAexrLNKZQucLo84ja4x4NEPY3bJiqW8o0qXZRKGZixT9v5rCXgZ6Wri1fPzNd2j4dl3594dtAY8V8zsg/UiJYqi+fMvLi4SCoVqxmzxeBxBEOjq6rri5zfw/PPP8+KLL/Lkk09y8uRJnnrqKVODqWkan/rUp7jtttveUTZKjQL1HoCqqkxMTNDS0rIlz69oNIrT6cTjD/D/JmarOqNKjHTpZquVN4Kgx2kuzI38JlEAuaiaeqVMTjb1JpLNym0j3VxYXK1rOptIJGgNBTiwo48T5+awWkSCdW60pZKKKAjMrSbLgYt62FylnuvO3SMImsrzr7xuFiBDz6Ib0Arcvr2XTE7vRjbaLaWyujFpR5Of8/NRFmL1u59mv5vR7haOTtQu/l12G00+N21BDw7JilJUsUtWSiXVDHNMZvPEUlmGO5uRi6W6HVAikcRus/KRAzuYXl5jdkUvhnarlbBfd+kwxmeiIKCBfiPPFUhnC1VBlH2tITqb6hcgA3v6dTbkyYsLNew2q1XvShFAVkrMrCRMca6sFE1hq9/l4O69I7x08ixLsYTJXlwXt0JXk59tbSFW4mlcDlv1+Kx8WLJbLXgcNo6ena0ZkSaTKUqlIvfePka+oPD6hvGlvit10Rr00Oz3oJRK+iGkoms0ui6rRWR7TzMnLyxsage2rS1MR9jL0QqWYcDtIORz4ZKsuOwSjvJh5mqKVKlUQlEULBYLoigyOztLR0dHTRcTjUZxu91bOowaLL5z586ZMe9Hjhyhp6cHVVX57Gc/y549e8z//7Of/Sx79+696te5nmgUqPcIMpkMU1NT9PT0XHVrrmkaMzMz9PVtYy1b4OxcLaXZ45Bo8rvobQmhlEoICFU0buPULxeL7Opr5fR0pC7zDyo9/2ZM+yGT5u5yIFktuJ12cxFs7KH0eG9jYV5k/0gPiqLwo1cnUBS5Rs/lcjq4a1c/sysJFmMJwpUuCBVheQIC8UyelUSmym5J0/RRy67hPoa6mnnl9ExdJh3obhUWUSw7Y1feaDH3LAGPg1KxxMmLi3Wfxyjel5ZWmYtWF29BABslRno7CZYZaOvjuequN+h16iO4tyhAFotg6pYEdNKFQUpx2o3xn+4SUeVtl8szv7hEcyjI3XuGOHbmEpfml2vyuWw2iZ62MMOdTRw7N4vdaiXkKz+/4aZfPmwIgsBcNEkqm68anxk/+/6hbuSy0LcSmqaL1/0+Nx8e304ymzP1eRs1ddmCQnvIw7n5KEubHDZ6WoL0NPs5enYGZYMbhdHVbWvTd8aqSs3fQHQtQSqb59btfVjQrpg0AVTpo3TXl1oXieXlZcLhsJkL9V5Ho0C9h7CwsEA+n6e1tfWqWT6yLLO4uMjQ8DDzq/ppvTJV1dCbZPIKzX4XFxZiLK0l6+6JOsJ++tuDvHy61gDUsCvq7whjFQWKJa280F53y05m8yxGouzb3k8mV+Bnk3NVEeKG71/A5+Hv3bqTc7PLLK5lEEUBEQj53AQ8OsPQaS+P7SrGf6mK8aVcLNHTEqS72V/3hl4qlVhejvD3P7AXp2Tl2Lk5U/xreNsZbuuaplEsqcybXV0BuWIc6pD0HdDk/ApLa+m6v4eQ183Ovhbmo0ncDltV1ygXSyQzOQRBJOB2cOL8ghlYuBF7BjqwCAIn6iz+3Q6JZr+bvtagzrQThBpSSjpXoFhUuaWvhTcuLjIXiVWN5wRBoFgssmukn139nbxyZgqlpH8WHOWuzjwMSLqmSEMjm1dMk2EjOgMN9g11UVRVTtaxXYKy7+JINwuxJDOROE1ly6vKrk7TdE1bKpdneS1japbUis+o0bFVHo424pbeNvxOiWgqi8dZHlFXfEZTORm/y06ppNtEVX7GNU03dm5pCnHX2CClonJFabwGZFnWo2sWF+nr66t5fH5+np6eni1NSt6NaBSo9xBUVeXcuXOEQqEtuRzH43FEUaStrY3VVJZ4WbS5Uc/S1xqiI+zlp6enN32usfJiOpbK6rEcG+yQ0nkZn9NONq9wZi5CvlCsonHncjk8TgcP3LmXo6cvsBLPmCdzo0P0uez0tgQJeZ3k5GLVniWT18WbmbyM322n2e++7PXuGehAEOBnFbZMRry9xyHhsttwOexV3naVHUW2oMfR7x/qvHz3WKZhHzs3i6pqNPndpomuQRrRdNtzluLp8mvoLgiqpiHLMqurMe6/ax9oWl0fPdAX/7eN9pDM5lDKzvSV7LZsQSGdU2gJuJiJJJhdWTPHc8aerlhUGOztZO9QN//32BkUVUOSJHM8VyoVkVDZf8sAdqsVpbR5V9ffHqpxJK+ErVyAlmLJKvJL0O0k6HPiczpwOdYPG4aUwTAaTqQzzM5t93Y0AAAgAElEQVQvMn7LMEOdTZfdlY72tBJ023n5zAxep0TY6zadUozPkKE3mo0myeR05/7Krk6yWTkw3MXCBpso0JOWI8sRBno72T/cg3yFabyappHL5chmsySTSbq7u2uIT9PT04yOjm6ZyfduQ6NAvceQz+c5f/48PT09V/0h1jSNubk5Oju7yJeooSNXYt9QF7JS5I2ppRq7GWO0AvqOIpJIr5+YK/KhPA47Hxwb4IVjb7KyljJV/obtTDKZZLivgx297VxaiuFz2XE7pAp2m0amoDt5u+w2Tl5arGEXGtg/1LXpfsdqEWkNehnsCFOQ9e7AuJEbYYixZBpZKTE20FGX4WagPexjsD3MKxPT5ohIFCHkcRMsm9y6HRKCAKIg1uxBDFLK+FAXxVKpZqQFOpMLTeXe28dYWE1waWmNoNtpjs/sktWMtqBstBpJpElnZTOM0uiGulvD3NLXzl/++AR5RbfQqfwdiKLAcFczYa+TxdVUzY1cVkqksnlcDjuCoPHapaW6eWKG79/GAmTAKVnpbg7QHvKRVxSslkrShTFCLiDZLPS1BDl2bpb8hggQw/Xi4K27CHtdvHxm/UBiMDwDbgfu8r5UQF+lZQvlrq7iMGApM/uW11KcX6gNXQTwuRzsGWjnzIx+IHHbJdxOCa/Tgcdh08eYNivF8ujOgCHSrYznMJh8kiSZAnsjqqPy+6anp9m5c+f7IqwQGgXqPYnl5WWSyeSWsqOKxSKzs7MMj4wwubDKcsUoSiqHBAbcDp3mW17Ib3SDNmjQXpeDsW1t/N2rZ4mn0lU0YkmSsEk2tvd20NMS5OXTU4gVbuhuh810W7eIgq5PSmbNE3mqfCOHdSukZCbHmdn62UR2ycqB4W4Wyk4V9bq6bF4h4HFwaWmN5Xi6ajxnjG72bh+kvz3ETzfZ73iddnb0tmKz6jfvel1dOi+zrTVAJi/XeAeuv9d6lMj0cpzZlXU2o9Nuo8nnwmkVCfk9WC1WLBah5kZuHAbaw14GOsL88JVTZHJZczxnkkYkib1DPQQ8Dl45M7N+I/c4zRGvzWIBQe/Ql+KZGtJFPJ7ALln5e7fewsJqgoubiKQ9LjvjAx3MRuJINusGJxD9MJBXigQ9DiZmV1hNZuqOkIe7mmnyuXj5dK03YzqdJuCyc/uuIdA0iqpWw/A0HNdHu5uJrKWZ3CQM0eO0Mz7YwcRshEh8vSO226x4HBJup52OkBe7TSd1lNSSTq1HQ1VVMpkMy8vLNDc3I8tyjeVYZTSH3W6v+lutx+xTVZXZ2Vl27txZ93rfi2gUqLcZb+WH9eyzz/Ld734Xq9XKL//yL1+VkWzla5w/fx6fz7clx+NUKkU+n6ezq4tMTsEuWWr0MumcjCgKdDf5eenNKfJyoYbGLVpE7tg9Sovfw49eO2/SuGF9dON12vG5HGYGj1yxkE/nCqylMkSiUX7hrv0sxmrHKQacDolbhzo5NbXMaiq7aVenaRqZvEI8kzNvVpUmt/1tYdpCnrrjQGMfdd+d40gWCwuxZM14ztB02W1WZKXIxPxK3a7O2EedX4iyWGdhbxVF+tqCdIZ9ZPOyLqas6OqSuQLRWByf10Nn2MdLb14iWyhUUbkN0sjd4zvwuez85NQlbFY9wr3KUdxpx+PU6cyGZVGqXOTSWb2rEwSBAyPdzK4kmI5UFyCDTNLT0cqB7b28MbXEWiqH32Un5HPVkCI0TSOVlVlL1zqBAOWOrboDqoQA7B3qAk1jJZHG79LHfzZL2X+xWCKVk/G67GQLMhNzUXJ1tHlup8S+wU7Ozq6wHK/dCVpEwWQ8RuIZPA4bLoeEpumfBQHNHAUaLDwjrLBQKCDLsrl/CgaDOBwOHA7HFZOYjOc0ipQsy6ysrNx0+6G3E40C9Tbjhz/8IS+88IKpRfj6179u+mGtrKzw6KOP8txzz1EoFHjooYd47rnntuRcXCgUmJyc3FJ2FOg6jNbWVhxOFxNzUd3OZgONW5Zl7h6/Bcki8H+Pn66hcQuCzv7bO9iBUlQpqWqV3YyxMM/mZQY7wlxcXGW+DvU8mUwR8rn5wK4BfnZ+nlRu/WZjnPj9bgchjwuLRUQQMEkdleLcTD7PYEdzDVV+I/ZVjNdEUScuBD1OvA67GYFuKUdDrCZzVaQLQ9PlclzBPqrMZpyYjeAtj4Yc9nXSRUEpUSyWcNp1d+3134Gu6crn8mRzWe774D7sVlH/HVRQuQ3vOa/Lzp7+dkolzdQTVbLbUrkC2YLCUEfYzH6qB0N/Vimc1X8HVkI+B06LQHtzSI8DEURKmv47TpUPAgYpYrirhZBn83woARgf6jJ3Voa/4Lr/ol6sRUGgpGpEEhkzUFMfkWpEIhG62lu545a+TQsQ6DvB7V1NvDm9hEUU8Tjs+NzlUbLFQrFUQo9C1rsiw56oMjnXSM+tHM85HA5sNhuCILC0tITVaqWpqWnTz9xmMP7erFYr+XyedDrNwMDAVT/PuxXvj03bOwiX88N6/fXX2bt3r2mn09PTw8TEBGNjY1f9Ona7nba2NpaWlujs7Lxql4lwOMzFixcZHBpClfNMTetLfZvNau4nnC4X5+aj3L69h1t3DZIvFOuG2WULRVx2K5F4nsX51Rq7GYBiSWW0u5loIlPlNA66MedSdJVoIsuegQ7SObmuOHduNUnQ40SyihzbxDXg3HxEd0bvbq4ZB/pcdkJeF6qq4nPZueuWPt1Voqh3dWsZnTSyuLKK0y5xx85+5lfjJDK1mplsXmZyYZXtPS3mPqqeY7wo6o7ZqZzeNS7HM6TKjvGKot+cPrBrgPagi9fPTFaN59xuF3a7nZdOnuH+O8f5wNgI8Uy+xlLIKNYuu41EqsDs7EoNuw2goOgSgXg6V3UIMJDK5FhJZNm9rU3XJ0m6Y/k6KaLAudll2sIBPE6JVzYpQOdmI+wb7q7xtwPMrktVVTxOuxnPYfoLVvgvWi0W9g126F12xQhOEKCpuYnpuQV8bic7eltJ52UyeRmbRcTtkPA47fhceucoigI7e9soVnRFalEhJ+tdkFGIDCNmi8ViFqJAIIDdbr/s31drayuzs7Mkk8mrnmhUGssqirKlw+a7GY0CdZ1gmDj+7Gc/Y/v27Tgcjrr/3+X8sNLptBnVAbpfXjpd/+R3JQiHwyQSCRKJxKa6CVVVqyI58vl81Yx8ZnqaHUND5Iq6XZAhfAx6nWbYnCgIdDcFUIoqybJvm2E3Y+xxupoD9LUEODcXqWvKuZJIE/a72TPQwemZCGGva8NCvh+lWKKk6uOxC4sxMxm2EgvRBLdt72FbW5BLdXYhejTHCmN97abVT6WlU7ZMs17L5Olp9nP83CyZfPXS32KzM7u0TGs4wM6+9hp6unHi9zntaGjcNtpTzo1aZ7ctrqVJZ/Vd3Z6BTmRZ4dWJSzXjOZvNxrEzU3xo7zAf3LuDS8v6z2Q4cnudDiSbiFXUiR5NPjdr2Xz5d6CPSQ06tdGxXVyI1hQngLVUlplIgrF+nQgS9DrxuR04NzhRyGVW4Nn5VVK5fBUpIpPJcnZqno9+YE9d3z/QiQkTM8uMD3Vy65DuiGDEfxhdVzJXIJrMsq0tuGk8R4EiE7NRRrpaSOeqQwytFpFtPZ2kU0nkYhPjgx1oGmUWph4dL6B//rPZbBVpwfgH66SFKzVirgdBEOjs7GRmZgZJkja9N2wGw1hWUZSr/t53OxoF6hqgaZr5YTVOUN/73vfo7+83Qws3wuPxmHEcoP+BGGy7jY9lMpmqgnW1qMyOkiSJ2dlZ05i2UCiY823jNOjxeAiHw1Xsv0gkQnxtjfGhToAqk9jKsLmuJj9hr5NTmzD/5lbiNPnc7O7vMKnGDquVUJl04bLrC3OLRWR8sNN0odAzqApkcgUy2Sxqsch9d4whCtTVABVVlTenltnd30YslcVmtRLyOPE47Ngl/SYoCAKFYhGv08HMit4BVZIuDFgtFsa2tdeMogQBmsJNHHt9grYP3cqB4R6yBQWnXe8oDHZbOi8zt5KkLeQllc3x5tRylZ7L2NWtxeN89I7dbGtvYiGmsxmNXZ1TshL2u8kXFLqbA3Q0+Ws0S6lYgbnFZbramhnpbmFyLlI38nwlkcbncbB3sNPcsdU1chVF9gx0mE4U0WSOdG49B0ws76OafU5W4tX7M7fbRUEu8NLr57ln3wg9LQEyuYK566ruuoo4HTaiiSyLi7G6vwOlVGK0u4VUrpa1B7o5bcinhxjORhP4XI6yvZaVklpClhXSiTX8fn/VeK7egcwYzbnd7hrSwrXCYrHQ2dnJ3NzcFY3dDZLExmu9lvvBuxGNAnUN2Bgq9sILL3DkyBH+wT/4B0B1ATMwPj7Oiy++yP3338/JkycZHh42HxsbG+OP/uiPzAXrhQsXqh6/Gpw/f54XX3yRc+fOMTk5ST6fp6uri8cee4z+/n4CgYA5I78cmpubmZ6exuv1kSoonJparkvjPj+/Qmikh5GuZs7OVY/ORBHCXjeyotDs9/CBHb0VdjO6OHe5nFGkoTG2TXfL3uh67nQ6ia2t8fqFecYGOomlMuaN2O92mB2F065Hc4xt66CkquvjuWjBtFwC2NnXRrPfzdRyfdbZhfkVQuWk3guLqzRVjecsWC1DlFS1HFWuMR1JlK2dChSLJTOj6LzDzof3bceiykSTyfIp2o7X6zV3dWfnVrilv4OWcBqntL5ngXWqe0ZWyuy1qZoCJNrsnDxznpDPzfhgV90dW9DjBE3FZhG585a+GiNXo+vKFRT2DnaQzOTrMtxUTePkpUVuHeqiPeQ1SR6Ga/zOvjaksklvX2sQVdVI5WTimQLp1VSV/19nk5/+thDnF1bqOr0vxVL4XA7GBzs5OjGL22HD7ZDwuhz4nBKusoO8qml0h736eE4tksvJKIpCoVAgFouxtLRkxlQYhajegexGQpIkWltbOX78OHv27MHpdJoEi8p9VqGg66ZsNptuQebx0NLSgsPh2FIO1LsZDZLEFvGTn/yEp556itbWVg4cOEAwGOSVV15BkiSeeOIJ88a/8cN/OT+sn/u5n+PZZ5/lmWeeQdM0Hn/8ce69994tXd+xY8dYXFxkeHiYbdu2sbCwYIYkXi0KhQLLy8sMDg3xxqUl4ptogNwOiX1DnUTW0kg2q9lRWC0ihWKJTF4mL5doC7p57dIiiXT95+lpCdLd5Ofl01M1oYGS1YJdVBkb1G1gVE2rGg0ZC/l0rsBIVzPKJtonWHdGj8TTptalKvDPofuqGcU0Wy6mlaSIyEqU1nCQO3b283cnzhCJxavGcwaVu7c1zGCHro9y2SXC5WLqsJfZbeK65c9sNKGzGDew20B35rZZLByfrN2x5fJ5Muk0H7tzHKVUoiAX9Rj0DTlIqZxMe9DDSiLDubn68SgGw+30TITohvGa4QbS2eTH65SQi2qVADiVlUnm8swvrtDX2UpPS6AmIbcS23ta8bvtVTsrp2TD45TwOOz43Q6CXieqplEsGuO5tyYt2Gw2HA4HkiQRj8fx+/0EAoG61/B2wOiKnnvuOY4ePcqv/MqvmOGiDocDp9OJy+XC5XJtaZT4XkSjQF0Djhw5wtmzZ0kmkxw5coTZ2VlsNhs7d+4kmUyyZ88efu3Xfu1mXyagd3sTExO0t7dvaY4di8WwWq2Ewk28MjFbZs9t7Ch0mrUgwGIsbRYKwwXBwGh3C36XnaNnZzd9vfHBTkQBkrnCuiO6VURALxSJVJamgId0Xub09HLd07dpTLuwykKslh3odzvobPLT7HNRUHSX78rxnEF1l2xWBtpD/OSNC6SyOZPKrd9cBIrFErftHqW3NcRLb15CKJ9yHZKVJq8Lf9kx21FOt9XKAuNUmXmmG93KuuXPcBeycrmiKnLbaDeReJpLSzFCPpcuAHbYq7ouAYFMQWYpljLdLiqJKZsx8irRFvIx1BFmMZbEXS7WBoOxoOjEFBAIeOwcPzdvdqYGCgWZtbUYf++OPTglG/+vzu/bZhHxuuzs7G0znR+ckhVV1Sip6jppoVyMjLGXUYyMMfVGTdFGKrcRLbOV7LSrRWVXZIhwja5IkiScTiff/OY3aWpq4vDhw++7ruhq0ChQW4BBiKjE5z//eQYHB/n4xz+OzWZjbm6OV155hYceegi32/2OOA2lUinThPJq/yg0TWN2dpbe3l6kcgRATi6u29mUT/zFksr4YCclVa3rggC61ua20R6iyQyT81Ez48fsKMp7HIC8XGQ5nq5yRNd/ljRel5279wxf9ibb7PewvbuZ6ciablnkkMxianRdxZKK3+3g5MUFUll9PGfQ6GVFoagUuWt8B0Gvk789drpM416n0pdKKnahpItDgZKqVRVTUxyakxnpbiaWzJhhihuxmWGswTD0ufRdkdWiW/7IVUaueiDfzNwiw9u6Gevv4Pi5WXJ1djcA3S0BepsDvHxmBptFP3AE3I6q90jTjZdYXE2Vu9N8lW4M9MA/AeoG/qVSaUrlvWE6V2AlmcHrtON16lTuddICVV2RQVqo7IqAGir31XQasiwzNze3JZeVejA0UJXXaXjpWSwWsytyu904nc7y50W/1lKpxGc+8xmeeOIJOjs7r/la3qtoFKhrgHGye/bZZ/lv/+2/8e1vf7uuDX69XdTNwszMDJqm0dzcfNXfqygKc3NzDI+McnZupS6zCtZvspPzUZYqAvoqadZep72sZREpqeqGjkLXyzT5al3PDWgaRKMr7B7pZ1t7mJdPTUF512VYChldlyisO1FUjucKStHshu7cPUSxWORvXnm9ejxn6LpEnRigG5DKdQPtktk8Qa+LeDrH+YXVmo4C3lofJVktbGsL0Rb0kC0odRmGqVwBh81KV7NPH51t6B4NQfFd+3bSGqwWHYtCha7Lacfl1C1/dNulihFpuXssaaoehFgnysKA1SJy20gPy3HdFshus+B22PE4Jf19som4HXZUTdPHmBVdUalUqqJyFwoFk9VaWYgkSbounUYmkyEajdb1ubscjGutpJzLsly10zICBnUNWqMruh5oFKjrgP/wH/4D+XyeJ554gmKxiKZpHDt2jHg8zv33329a6L8TcK3ZUclkElmW6ejUl9b1HKGtoshARxOtATfpvFxtZ1PRdTkkG60BNy+fqt01GRjtacXvlGrGgX6Xg4DHgdMq0hz0oQmYThSZvG7uaXRdBbnIbaPdrMRTHD9zqWo8Zwhb3S4nd48NMBOJM7MS1wPtykaubrtk0qARdL3QajK3bilUHmHGYjE625q4daSXE5O1oXYGOsI+BtrDnJ2N4HM76rDbFIqqhttu5c3pCKlsLbsNYGdvGy5H/dFZoSAjlArcc+su0DSUkrqp7dJge4jVVJZzc5e3idoo4rWUY+rdDomWgJegx4Gq6h1XpdNCqVRienqaYDCoMygryADGDd64ydvt9htOWojFYhQKBdra2moOjkbhrLfTMqQXlV2RQbxo4MagUaCuAUZnlM/nEUWxyvHhf/2v/8UXvvAFfvrTn5rU7ncKriU7CnTL/9bWNlTRqu9B6kRPFBR9mW21iEyUhaEbF/6guzZcjsjglGzsH9aNaUuahmSt1sskMnliiRQ7+zu5tBRjailmUrllWaZY3mu0hIPcs2+UV8/OEM/K5njO6CgCHidhrwubzVLuKNYZhkbXlcrlaQl4GGgP8/Lp6Zqlv6pqRCLL3L57Ox1hn9m51LNdsllEVE0jkSmYhWKjpmh8qAu1pOdH1YMoChwY6SGezrGWyhL0OmsEupm8jNshkcwWuLi0alLFK2F0dWdmIpt2xR1hP4MdIRai+j7K7Vx3WjBIC0Yx2ozKXSwW8fv9uFy6wFiSpJtyc9c0jR/+8Iesrq7yiU98oqorUhQFQRDMQmQQF27Wtb7f0ShQ14h63dFf//Vfc/z4cYLBII888sg7UrswPz9vniKvFsaJeHR0O6IokswVaqInNE0/Yd8+2stCLFFXNAvrp/MLC1HkklqhWbKaMfE5WcEhWYnE0yytZWrGc+l0mp72Jm7fOcT/99JJFFUzx3NW67rlz2BHmPaQl0QmXxODbnQUTslKwOOoa0RqYGdvG067tcatwmoRCboduCQLvW1NumZIFNA0asx0cwWZ/cPdrF5uH2W1cGC0h5nlNWbKhrHVWVRW3Y1C0G2X4pm8GT+hv0clotEVejvb2D/SU2MTVYnWoI/hzjCvnp/DZtEDI31OO16XXSctaJou7tXUuqSFyhu8oa2rJC5YLBZzvFYviO9GwrjeStJCMpnkt37rt3jkkUfYv3+/yZ4zuqIG3hloFKjrAGOpa7FY+OM//mNSqRT33Xcfu3btuuGMoa1CVVXOnj1LOBzeUnZUJpMhmUzS27eNE5PVKv5KGGyxypGX32Uvx7jrmiXJqi+PiyVVDyysGM/lCgpKUWFbW5je1iDfP3IcWV4fzxm7okQ8zl37dhL2unj1/Fw5WkHvKCqNXEuqhijAhaW1KvGpAQHYP9xNTlZ4c5Odi0UUuWN7DzlZoVTSql3RyxHua6ksg53NzK7EN9VZGZ2LYXBbCYMB2Bry4bJby8QLi5lFZRSiVC6P3+VgsCPM0YnpGn2UkU1029go3S0B0/VCEMBll/BU2P743Q4zdHEjlXtjPEQlK62yEL2Vtm51dRVFUbZ0MLoSbGT66Vo0pYrKbXRFsViMxx9/nP/4H/8jHR0dN+R6Grg2NArUdcCPf/xjnnzySfbu3cvIyAj33HMPnZ2d7/iRQDab5eLFi/T29m5p1Le8vIzf78fu8nDs3CwbP0kOm06K6G4JYLOI+k12w8Lf2OP0tgRx2a0ceW3SdFpQFL3oGTlRHxrfXmYHLpmO3AGvbiLqLRciu2RDFCCvlMzxnEF312PS9SC/+Whi08Jhl2wcGO5icj5KIpOjye/GXx7PVWqKLKJAPJ3T/fM2uKKvrsbo7WhhfLib4+c2L+CGUHV5LVXjdpEtkxYsgkDQ4+DoxIxpRrsRoz2tBFz2ugJdQVPRijIf3DOKqqpoGmWnBb341CMtVBaiSlZaJZV7K52GpmnMz8/j9Xrx+/1X/f2Vz/NWVG6jI7qcwHViYgKr1crg4OCWr6WBG4dGgbpOeOKJJ1AUhT/8wz+8Ls/3VrEcv/u7v8urr76K2+0G4E//9E+3NEpcWloinU7T3t5+1QXV0JYMDA4Sz8iUVNW8yW5MVvW77BTKAYeyoscIGE4LsqJgFUV+4eB+phZXODe3UjOeczsk2oJeupv9FBRd3LjRkXstlSGbzXPbLdt4c2qJWCpX97oDbidj/W28OjlPutzVbXTMdkr6awvCupODXkzXNUXdzQF6WwJ1s6FUVWN5eZk7x2+hJeDh5TPTeJ0SIa8b/4bQP8MXbzaaqKHTG9g72HnZBF1RELh1pJtsXjap3D6nHZdDQgAKskwhn8flcm5K5TZC8yqLkBEPcT0PW8bn5ko1eZWkBaMQGQLXyo7I6XQ2BK7vMTQK1DXC2EGl02m+8Y1v8Oijj14XtfrlYjkADh06xNe+9rVrJmCoqsrk5CSBQGBLBS6fz7OyssLg0BA5uUi0bJdTOZ5TZAWnZOVD4yMcOXGGpVi8ajxnxLgb48DppTWcZUsbY+EPuktBrlAk7HNyeiZCLJWtMT1diUbZOdjLUGczL5+ZoVTHvcDvsjPY2YzLbkMuFmv88wxNUWvQg9dp5+hlojl293dgFQVOVGiAbFaRJp8bn1PCKVnxul1V6a2pXEGPAcnnyeZkEOC2kZ7L7qNs5c7PyGNySNaq8ZzbYUeyWspdUck0QjX+GW4glTocm81WQ+V+u27usiwzOTlJX1+fecgyXLs3Zippmobdbq8qRFvt4Bp4d6FRoK4DDOHuVuz0N8OXvvQlxsbGeOCBBwC46667+PGPf2y+3p133sn4+DjRaJRPfOITfOITn9jyaxnZUVsVMK6urmKz2fAHQ/zt8TPk87rCX/cTs5pU7sGu1qo02kpHbmOPYxF1+6JYKle18K+ks29GPQd957K8tMx9d45js4gsxlI6VbwiKt5gAEpWfS91aiZCNl+oGVGKgsCB0W7WUrkaf0EDzX43O3paKZTZghsjQNZSGZLpLHuHe7iwuMpCnbwr2HwfZTXiIRwSrUEvXpe9IiSv1mmhXmieQVqQJIlEIkFra6tZFG4GjOs9cuQI3/nOd/id3/kdisWiedjb2BVd7w6ugXcPGmax1wHGSe56FSe4fCxHNpvln/yTf8I/+2f/jFKpxCOPPMLOnTu3nLRpt9tpbW01s6MudzOoF89RLBYpFovYHQ72DHZzanq5KjDPZbfpAl2XA0EQ+MCOPixitTfc4lpKH20VFPYNd6FpGjOR+juic7MRbhvtYbiziXPzUUQg5KsQ6O7oM4uds93GajLH0lraHM8ZmiKDQehzSmRytZlOqqbx+qUl9g91kszmsFgsBOrsopLZAl6XxOxKkqV4qia9NRpdRbRY2D3QSSyVrevKncvLzK8m2dHbysJqAq/Lgdthw1p+nzRNRQDksiannsHoxtA8v99fQ1rwer3Mzc1tee94tTBGiRuLpiAIjIyMsHPnTr73ve/xuc99rkHlbqAGjQL1DsXlYjmcTiePPPKIyRC8/fbbmZiYuKYo6KamJjM7KhAIoGnapqdxg7lV6QYtyzILCwsMD4/gdEhINp0CvdGR+9LyGttag1xcXN00ufWNqSUODHfR5HfXGJUaexy5WKI16KEl4KmiisczBdL5FEuRVdxOOwd29DG9HKtLUijIRSbmoox2NbGazCIXSxvMYnV/O4ChzmbycpFktsBiHX87PRrcy/TSas3rhEIhzl6coTXoY+9ABycm58uhebrTgscp4bDZKKkqmqrSFnDrHZKioGxyIDBC8xwOxxWF5hmQJInm5mYWFhbo6uq6bgWhksq9sWharVazKwqHw7hcLvNav/jFL/Iv/+W/5OzZs1sK5mzgvY1GgXqH4nKxHGePfPUAABLBSURBVFNTU3zmM5/hL/7iL1BVlVdffdWM+NgKYrEYZ8+e5fTp0xw7doy5uTn6+/s5fPjwZU/jlZAkiUAgQDS6QmtrK/OrSWKpeF2Bbr6gsL2nheW1dF0ninxB4dLSGtu7m4n6XeWsKKtJFTf2OJm8TJPPxUtvXqK4YRcl2iSmFpboaA6yu7+Dl89M17yOz2XHbbeiqiq3jXSjQdUuqjK9daSzGclqYWI2Uvfnn1qOEfI6GRto5+QFXVgrCutOC0MdIZw2AYdk4/btPWZoHpqGpqnkctkaKrdBWjAOBNcSmlcJr9dLLpdjdXV1SzHk9bKKNgpcjUL0VrRzURR56qmnGp1TA3XR2EG9Q/FWsRzf/OY3+eu//mtsNhsf//jHOXTo0JZeJ5lM8qu/+qv09fUxPDxMS0sLXq+XwcHBLRnKzs/P097RgaKJm5rFgh6x4CvvkYJeJyFP9S5Kz1hSQYOZlYRJvFA2FLTxwU5UVa3rtlAsllhZWeHjH7qVYqlEXi7isq/roirp7k0+F+lcgTenl2p2UaCz/G7f3sPiapKLS7Gaxx2SlaDHyUhXM6lsAclmQbJZy/EQ+ngumUySTqdpamqq0RRVphhXsuhu1I1b0zRmZmZoamradB91JVlFhsD1/ZhVdK147bXX+IM/+AO+853vVH39W9/6Fn/+539uEqB++7d/m/7+/ptxiTcdjQLVQBU0TWNqamrL2VHFYpHZ2VmGhke4uLTGYkXMReUuylVm6ImiYO6iTFJEXtcUWSwit1cw1+pBslq4bVQnICytJgl4nbrTgtOIn7CU49YhU5BZXkubxItKTZGRZfXG1BJrm9DTDZbhubkooijgc+mu3E67rYK0AJqmVpEWjEKUz+fJZrNYLBbzpm4UorcrNK8SiqLw7LPPcs8999DW1vaWAtdGVtH1wze/+U2+//3v43Q6efbZZ6se+5Vf+RX+6T/9p+zcufMmXd07B40C1UANisUiExMTdHZ2Yi9Ha1wN0uk0mUyG7p5esgW57i4qlS1QVDVGusKXteAJelzs2tZaI3Z1ldNbA259h2O16F2XoYtKZgtlAkaeuYVlhvs62dHbxstnpusarwJ0NQXoa9V1TZoKTrsNj9OOxyHhcxukBYtOUthA5X6r0DxjXySKIjMzM3R1dVV5N75d2ChwPXr0KH/2Z3/Gb/7mb9aw5xpd0Y3D888/z8jICJ///OdrCtRHP/pRhoaGWFlZ4UMf+hCPP/74TbrKm4/GDqqBGlitVrq7u5mfn99SdpTH4yGVSpHLZnC73ZyejpDaxCzWZbexa1t7VSREJVJZ3V9ufLCTnKxUFTsjvXU6kiDo1RNw62mWgsEgb567RFtIJyls9NCTrBbcDglB0L3zPri9D1EUa5wWdNJCoSYeQlEUk7Rgt9sJBAJIkrQpS669vZ2FhYUtvbdXiivNKrrvvvuIRqM8//zzfP7zn78h19JALe69917m5mpTkQEeeOABHnroITweD4cPH+bFF1/knnvueZuv8J2BRoFqoC78fj+JRIJYLLalRXprayvT09MMDg3hcUp1s48AppZWafK52Nnbymw0URFcWOmMXtQJDKLIubkoqXwBWakudkuxJLeN9jDU2cTkBrGrKAqEwyFeOnmGn79rH7f0tiIXS2WnBX2Jb5AWiopStgOqFY1uDM1zOp1bIi04nU58Ph+RSOS6eNLVyyoybKIqmX6bZRU9/vjj/P7v//47Khbm/QpN0/ilX/olUzR/8OBBTp8+3ShQDTSwEZ2dnUxMTJjZN1cDURRpa2tjZnqa/v4BVsthgbDu0RdwO8qUdAtOu4ug12U6Oej+duvO6IaQVUOtKU5Q1ixNLbFvsINIPE1BKZYFrnZ8bn1MJ1ktyIpCwO2A8p5IkeVN4yEqQ/NCodB1C80Dvaubm5sjlUpdsYNHvawiuXz9lVlFoVDoqrKKRFHkiSeeuNYfqYHrgHQ6zcc+9jH+6q/+CpfLxdGjR3nwwQdv9mXdNDQKVAObwmKx0Nvby/T0NL29vVd9c3Y6nUiSxNpajLFt7aiaWuPRt1wW0HqcEn0tAV6/uFjXniibl7m4uMaOntYq7zuLKOJx6lRun1NPbd3T316b3loqkpULzMzM4Ha7zRyvjamoldquGwlBEOjo6GB6ehqHw4HNZqt6/HIC18pC1MgqujZsxqR74YUX+NrXvobVauXBBx/kk5/85A29jv/zf/4P2WyWf/yP/zGf+cxneOSRR5AkiTvuuIODBw/e0Nd+J6NBkmjgLTE3N4eiKLS2tl7192qaxvT0NP0Dg8gllVMzkapQvkqM9bdjFUVerfC1MyCgkxZ293dQUlXkYgm33YbVDM1T65IWKrsNVVWxWCwUCgWam5vfETf3aDTKF77wBf7gD/6gykm8kmDRyCq6MdiMSacoCvfffz9//ud/jtPp5NChQ/yn//SfaG5uvolX+/5Eo4Nq4C3R0dHB2bNnyWQyV+3hJggC7e3tXLp4gaHhYVySddMCdXp6mdtHe+hrDZLI5PE4JLwuB16nhEOymaQFySJgFURKRQVFLtTEQ2wMzfP7/WZoHuhjlLW1NQKBwNtanDYTuI6OjvK1r32Nw4cP4/V6r0jg2sC1o6enhz/5kz+pIYdcuHCBnp4eMw5k3759HD9+nI9+9KM34zLf12gUqPcIbuSoQhRFent7t5wdZbfbdVLA8jLbe1o5OjFDsaQiCgIuhw2PQ09u9TrtiKJAd7OfzrAPTVNNp4V8PlcTD7ExNO9KSQsej8csUtfqBl8PlxO4GllFXq+XlpYWHA4HO3bs4PHHH+fChQvceeed1/16GqiPzZh06XS6ai/odrtJp9Nv56U1UEajQL0HUDmqqISiKHzpS1+qGlXcc889WxpVuFwuwuGwyTy72tN9IBBgbm4On8/P/qEuBAEkq5WiWkJT18dzctlVYSOVe2NoXjAYvKbIhZaWFqanp03B7Fax0Ty3XlaR3+9/y6yi3//932d5eXnL19HA9cNGH8xMJrOlKJoGrh2NAvUewNs1qmhtbeXcuXM1J8wrgSAItLW1MT09RX9/PxqQU+S6RABYD81zu903hLQgiiIdHR0sLCxcEQHkSrKKjEK0lcIZCASuS47YuwlvVyjn1WJgYIDp6Wni8Tgul4vjx4/z2GOP3fDXbaAWjQL1HsDbNaoQRZFt27YxOTlpdgRXCoOV5nA4mJycxGKxmJ5uRjHyer1vK2nBENWeOnWKXbt2AdVU7sp/G7OKgsFgI6voGvG3f/u3yLLMM888w8mTJ3nyySerQjlPnTrF008/fUPGsPVQyaT7whe+wGOPPYamaTz44INbIgg1cO1oFKj3MG7EqMJut9PS0sLy8jIdHR01N2dN06qIAIZo1CAt2O12FEXB6/USDAav6VquFaqq4nK5ePrppzl48CAHDhyoop0bheidwPZ7L+LEiRPcddddAOzZs4c333zTfMyIhf+N3/iN6xLKuRm6urpMBt/P//zPm1//8Ic/zIc//OHr/noNXB0aBeo9jBs1qmhubiaRSDA9Pc3s7Cw+n4/m5uYqIkAlg24jI83v9zM9PY3H46nR/9wI1BO4VmYVHT58mC9+8Yt88IMf3JKLewNbw9sZytnAuxONAvUexI0aVZw/f56/+Iu/4OzZs0QiEaxWK4ODg3z0ox+9KtKCxWKhra2NxcVFuru7r2tnUukgXq+D2yyr6Nd//dd56qmn+OpXv3rdrqWBy+PtDuVs4N2HhlC3gSvG9PQ0MzMzjIyM0NzcTCwWY2Vlha6uri11HZFIBIvFsqVYD4PKXRkPUSlw3UpWUT6fvyZGXwNXh+eff54XX3yRJ598kpMnT/LUU0/x9NNPAzrBpzKU8+GHH+Z3fud3GBoauslX3cDbiUaBamDL0DSNixcvml51Vwtjz9De3n7ZwlApcG1kFV1fvBWT7tlnn+W73/0uVquVX/7lX76upqVvVyhnA+9eNApUA9cERVE4e/bslvON8vk8//t//28+/vGPY7fbq7KKjKJUKXBtZBVdX/zwhz/khRdeMLuYr3/96yaTbmVlhUcffZTnnnuOQqHAQw89xHPPPXdTcqwaeH+isYNq4Jpgs9no6uoy90lXUjQ2ZhUtLy/z5S9/mYcffrgqq6hB5b7xuByT7vXXX2fv3r1IkoQkSfT09DAxMcHY2NjNutwG3mdoFKgGrhl+v594PM7a2lrNPmkzgSusZxV96lOf4nOf+xzZbJYDBw7cjB/hfYvLMekalj8N3Gw0ClQD1wxBEOju7ubMmTNYLJaqndGVZhV96Utf4umnn24UqLcZl2PSNSx/GrjZaBSoBq4LLBYLXV1dLC0t4fP5rlrg2tHRwW/8xm+8DVfaQCXGx8d58cUXuf/++zl58iTDw8PmY2NjY/zRH/2R2fVeuHCh6vEGGrjRaJAkGmjgHYJ8Ps+v/uqvsrq6itvt5stf/nINO/LTn/408XjctIgyaNlbxVsx6Z599lmeeeYZNE3j8ccf5957772m12uggatBo0A10MA7BN/61rdIp9P8q3/1r/jBD37Az372M/7tv/23Vf/P/fffzw9+8IMGaaSB9wUaPN33IV577TUefvjhmq9/61vf4oEHHuDhhx/m4Ycf5uLFizfh6t6/qGTU3X333bz88stVj0ejUZLJJJ/+9Kc5dOgQL7744s24zAYaeNvQ2EG9z7BZdhTo7tFf/vKX2blz5024svcXvve97/Htb3+76mvhcNgkIbjdblKpVNXjiqLw6KOP8sgjj5BIJDh06BBjY2NbcuK4GqiqiiiKqKpqMjUVRcFisTS0aA3cUDQ+Xe8zGNlR9XDq1Cm+8Y1vcOjQIb7+9a+/zVf2/sI/+kf/iL/8y7+s+uf1ek3WXCaTwefzVX1PU1MTv/iLv4jVaiUcDrN9+3YuXbp0Q65PURTefPNNJiYmEEWRSCTCpz/9af7sz/4M0PVvjeLUwI1G4xP2PsO99967aY7TAw88wG/91m/x7W9/mxMnTrxvR0h/8zd/w+c+97m6jz377LP8w3/4D/nkJz953d+f8fFxfvSjHwFw5MgR9u3bV/X4T3/6U/71v/7XgF7AJicn6e/vv67XYCCVSvE//sf/4Itf/CKgvyfpdJrDhw+zvLzMn/zJn/Bv/s2/4fd+7/dQVfWGXEMDDTQKVAOALqj9pV/6JUKhEJIkcfDgQU6fPn2zL+ttx+/+7u/y1a9+te5Nd2Vlhe985zt897vf5T//5//MH/7hH5qi4+uBQ4cOMTk5yaFDh3jmmWc4fPgwAF/5yld4/fXXOXjwIL29vXzyk5/kscce47Of/ewNC/MLhUL8u3/377BYLPz2b/82/+W//BeefPJJAGKxGA6HgwcffBCn08n//J//87q+Dw00YKCxg2oA0B0FPvaxj/FXf/VXuFwujh49yoMPPnizL+ttx/j4OB/5yEd45plnah670dY/TqeTP/7jP675+uc//3nzv3/t137turzWlcBqtfLrv/7rPPbYY3zsYx+jra0NgO7ubv75P//nACwvLxOLxSgWiw2PvgauOxoF6n2Oyuyoz3zmMzzyyCNIksQdd9zBwYMHb/bl3TDUIyn8+3//77n//vv5/9u7Y5bU4jCO49+GU1SCEQg1RYORGA1NBb0BB8lBBQ8lhC9AfAcNDm1Op6WhpaWtSYQmocXBs2iRg6AQNNgWGGHqnYoLdbv3djudc/X3Wc/5c57hwMNz/s95/pVK5d014zj6p91u4/f7ubu7o1qtsrW1hc/no9frYRgG19fXBAIBZmZmGA6Han+XL6UENYZ+dcx1LBYjFou5Fda3SiQSJBKJv1ozbqN/Op0O5+fnZLNZGo0Gx8fHLC8vs7CwgGEY1Go1bm9vyWazAEpO8uW0ByXyh9bX16lWqzw9PfHw8DDyo39OT0/x+XxEo1FM02Rubg7LsgB4fn6mXC6TyWSYnJzk8fHR5WhlFKmCEs+5uLigVCq9e/x6Pp/Htm1mZ2cBODo6cryKOTk5eR39s7e3h2maDIdDcrkcU1NTjj7bLc1mE9u2OTg4AGBxcZHDw8PXfaarqyssy6Jer9PtdkmlUkQiERcjllGkUUfiKfl8nsvLS0KhEIVC4c31VCqFZVmOda/Jx172mer1Ou12m5WVFZaWltQgIY5QghJPKRaLzM/Pc3Z29iZBDQYDtre32djY4P7+nng8TjwedynS0fdysKR+yBW36BOfuOIzXXTdbpfd3V329/fp9/uk02nW1tZYXV39jpDHzsTExIeND4PB4Lf3iPwLJShxxWe66Kanp0mn069zBDc3N7m5uVGCcokqK3Ga3jD5b7RaLUzTpN/v0+v1sG2bcDjsdlgi4hBVUOJ5P3fRRaNRkskkhmGws7NDMBh0OzwRcYiaJERExJP0iU9ERDxJCUpERDzpB98UXAPjMgyhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "with sns.axes_style(\"whitegrid\"):\n",
    "    ax = fig.gca(projection='3d')\n",
    "ax.plot_surface(xx, yy, zz, alpha=.25)\n",
    "ax.set_title('Learned Function')\n",
    "ax.set_xlabel('$x_1$', fontsize=12)\n",
    "ax.set_ylabel('$x_2$', fontsize=12)\n",
    "ax.set_zlabel('$y$', fontsize=12)\n",
    "ax.view_init(elev=45, azim=-20)\n",
    "fig.tight_layout()\n",
    "fig.savefig('surface', dpi=300);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To sum up: we have seen how a very simple network with a single hidden layer with three nodes and a total of 17 parameters is able to learn how to solve a non-linear classification problem using backprop and gradient descent with momentum. \n",
    "\n",
    "We will next review key design choices useful to design and train more complex architectures before we turn to popular deep learning libraries that facilitate the process by providing many of these building blocks and automating the differentiation process to compute the gradients and implement backpropagation."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": true,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {
    "height": "calc(100% - 180px)",
    "left": "10px",
    "top": "150px",
    "width": "254px"
   },
   "toc_section_display": true,
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
